physics.jsonl

{"id": "phy_0001", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 3 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 6 N.", "steps": ["F = m×a.", "F = 3 kg × 2 m/s².", "= 6 N."], "text": "Answer: Net force: 6 N.\nSteps:\n1. F = m×a.\n2. F = 3 kg × 2 m/s².\n3. = 6 N."}
{"id": "phy_0002", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 1 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 12 V.", "steps": ["V = I×R.", "V = 1 A × 12 Ω.", "= 12 V."], "text": "Answer: Voltage: 12 V.\nSteps:\n1. V = I×R.\n2. V = 1 A × 12 Ω.\n3. = 12 V."}
{"id": "phy_0003", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 15 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 288 K.", "steps": ["Add 273.", "15 + 273.", "= 288 K."], "text": "Answer: Temperature: 288 K.\nSteps:\n1. Add 273.\n2. 15 + 273.\n3. = 288 K."}
{"id": "phy_0004", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is reflection?", "choices": null, "answer": "Light bounces off surfaces with angle in equal to angle out, forming mirror images.", "steps": ["Light bounces off surfaces with angle in equal to angle out, forming mirror images.", "So the answer stands: Light bounces off surfaces with angle in equal to angle out, forming mirror images."], "text": "Answer: Light bounces off surfaces with angle in equal to angle out, forming mirror images.\nSteps:\n1. Light bounces off surfaces with angle in equal to angle out, forming mirror images.\n2. So the answer stands: Light bounces off surfaces with angle in equal to angle out, forming mirror images."}
{"id": "phy_0005", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 200 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 600 m/s.", "steps": ["v = f×λ.", "v = 200 Hz × 3 m.", "= 600 m/s."], "text": "Answer: Speed: 600 m/s.\nSteps:\n1. v = f×λ.\n2. v = 200 Hz × 3 m.\n3. = 600 m/s."}
{"id": "phy_0006", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 800 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 200.", "steps": ["Halve: 800 → 400.", "Halve: 400 → 200.", "= 200."], "text": "Answer: Survivors: 200.\nSteps:\n1. Halve: 800 → 400.\n2. Halve: 400 → 200.\n3. = 200."}
{"id": "phy_0007", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 2 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "6 N", "B": "3 N", "C": "9 N", "D": "12 N"}, "answer": "Net force is 6 N.", "steps": ["F = 2 kg × 3 m/s².", "F = 6 N.", "Select option A."], "text": "Answer: 6 N\nSteps:\n1. F = 2 kg × 3 m/s².\n2. F = 6 N.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0008", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 2 A flows through 5 Ω. What is the voltage?", "choices": {"A": "10 V", "B": "5 V", "C": "15 V", "D": "20 V"}, "answer": "Voltage is 10 V.", "steps": ["V = 2 A × 5 Ω.", "V = 10 V.", "Select option A."], "text": "Answer: 10 V\nSteps:\n1. V = 2 A × 5 Ω.\n2. V = 10 V.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0009", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 1 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 8372 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 1 K.", "= 8372 J."], "text": "Answer: Heat: 8372 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 1 K.\n2. = 8372 J."}
{"id": "phy_0010", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 20 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "2×", "B": "1×", "C": "3×", "D": "4×"}, "answer": "Magnification is 2×.", "steps": ["M = 20 cm / 10 cm.", "M = 2×.", "Select option A."], "text": "Answer: 2×\nSteps:\n1. M = 20 cm / 10 cm.\n2. M = 2×.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0011", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Vlna na struně má f = 200 Hz a λ = 3 m. Spočítej její rychlost.", "choices": null, "answer": "Rychlost: 600 m/s.", "steps": ["v = f×λ.", "v = 200 Hz × 3 m.", "= 600 m/s."], "text": "Answer: Rychlost: 600 m/s.\nSteps:\n1. v = f×λ.\n2. v = 200 Hz × 3 m.\n3. = 600 m/s."}
{"id": "phy_0012", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 400 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "100", "B": "50", "C": "150", "D": "200"}, "answer": "100 atoms remain.", "steps": ["Halve twice: 400 → 200 → 100.", "Left: 100.", "Select option A."], "text": "Answer: 100\nSteps:\n1. Halve twice: 400 → 200 → 100.\n2. Left: 100.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0013", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is Newton's first law?", "choices": null, "answer": "Objects keep velocity unless a net force acts, so motion needs no push to continue.", "steps": ["Objects keep velocity unless a net force acts, so motion needs no push to continue.", "So the answer stands: Objects keep velocity unless a net force acts, so motion needs no push to continue."], "text": "Answer: Objects keep velocity unless a net force acts, so motion needs no push to continue.\nSteps:\n1. Objects keep velocity unless a net force acts, so motion needs no push to continue.\n2. So the answer stands: Objects keep velocity unless a net force acts, so motion needs no push to continue."}
{"id": "phy_0014", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is electric charge?", "choices": null, "answer": "Charge is the source of electric force, positive and negative attracting opposites always.", "steps": ["Charge is the source of electric force, positive and negative attracting opposites always.", "So the answer stands: Charge is the source of electric force, positive and negative attracting opposites always."], "text": "Answer: Charge is the source of electric force, positive and negative attracting opposites always.\nSteps:\n1. Charge is the source of electric force, positive and negative attracting opposites always.\n2. So the answer stands: Charge is the source of electric force, positive and negative attracting opposites always."}
{"id": "phy_0015", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 500 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 50 W.", "steps": ["P = W/t.", "P = 500 J / 10 s.", "= 50 W."], "text": "Answer: Power: 50 W.\nSteps:\n1. P = W/t.\n2. P = 500 J / 10 s.\n3. = 50 W."}
{"id": "phy_0016", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 30 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 3×.", "steps": ["M = di/do.", "M = 30 cm / 10 cm.", "= 3×."], "text": "Answer: Magnification: 3×.\nSteps:\n1. M = di/do.\n2. M = 30 cm / 10 cm.\n3. = 3×."}
{"id": "phy_0017", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is a wave?", "choices": null, "answer": "Waves carry energy through oscillation without net matter transport.", "steps": ["Waves carry energy through oscillation without net matter transport.", "So the answer stands: Waves carry energy through oscillation without net matter transport."], "text": "Answer: Waves carry energy through oscillation without net matter transport.\nSteps:\n1. Waves carry energy through oscillation without net matter transport.\n2. So the answer stands: Waves carry energy through oscillation without net matter transport."}
{"id": "phy_0018", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Vzorek 800 atomů projde 2 poločasy. Spočítej přeživší.", "choices": null, "answer": "Přeživší: 200.", "steps": ["Půl: 800 → 400.", "Půl: 400 → 200.", "= 200."], "text": "Answer: Přeživší: 200.\nSteps:\n1. Půl: 800 → 400.\n2. Půl: 400 → 200.\n3. = 200."}
{"id": "phy_0019", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Těleso 2 kg zrychluje 3 m/s². Jaká je výsledná síla?", "choices": {"A": "6 N", "B": "3 N", "C": "9 N", "D": "12 N"}, "answer": "Výsledná síla je 6 N.", "steps": ["F = 2 kg × 3 m/s².", "F = 6 N.", "Vyber možnost A."], "text": "Answer: 6 N\nSteps:\n1. F = 2 kg × 3 m/s².\n2. F = 6 N.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0020", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 5 s. Compute the energy used.", "choices": null, "answer": "Energy: 500 J.", "steps": ["E = P×t.", "E = 100 W × 5 s.", "= 500 J."], "text": "Answer: Energy: 500 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 5 s.\n3. = 500 J."}
{"id": "phy_0021", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is temperature?", "choices": null, "answer": "Temperature measures average particle kinetic energy, felt as hot or cold.", "steps": ["Temperature measures average particle kinetic energy, felt as hot or cold.", "So the answer stands: Temperature measures average particle kinetic energy, felt as hot or cold."], "text": "Answer: Temperature measures average particle kinetic energy, felt as hot or cold.\nSteps:\n1. Temperature measures average particle kinetic energy, felt as hot or cold.\n2. So the answer stands: Temperature measures average particle kinetic energy, felt as hot or cold."}
{"id": "phy_0022", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 3×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "2 s", "B": "1 s", "C": "3 s", "D": "0.5 s"}, "answer": "Time is 1 s.", "steps": ["t = 3×10⁸ m / 3×10⁸ m/s.", "t = 1 s.", "Select option B."], "text": "Answer: 1 s\nSteps:\n1. t = 3×10⁸ m / 3×10⁸ m/s.\n2. t = 1 s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0023", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Hrom je slyšet 2 s po blesku. Jak daleko je bouře? (v = 340 m/s)", "choices": null, "answer": "Vzdálenost: 680 m.", "steps": ["d = v×t.", "d = 340 m/s × 2 s.", "= 680 m."], "text": "Answer: Vzdálenost: 680 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 2 s.\n3. = 680 m."}
{"id": "phy_0024", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 3. How many spectral lines can it emit?", "choices": {"A": "2", "B": "3", "C": "4", "D": "5"}, "answer": "Count: 3.", "steps": ["Pairs: 3×2/2.", "Lines: 3.", "Select option B."], "text": "Answer: 3\nSteps:\n1. Pairs: 3×2/2.\n2. Lines: 3.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0025", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 3 kg zrychluje 2 m/s². Spočítej výslednou sílu.", "choices": null, "answer": "Výsledná síla: 6 N.", "steps": ["F = m×a.", "F = 3 kg × 2 m/s².", "= 6 N."], "text": "Answer: Výsledná síla: 6 N.\nSteps:\n1. F = m×a.\n2. F = 3 kg × 2 m/s².\n3. = 6 N."}
{"id": "phy_0026", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why Coulomb's law?", "choices": null, "answer": "Force scales with charges over distance squared, governing all electric pushes exactly.", "steps": ["Force scales with charges over distance squared, governing all electric pushes exactly.", "So the answer stands: Force scales with charges over distance squared, governing all electric pushes exactly."], "text": "Answer: Force scales with charges over distance squared, governing all electric pushes exactly.\nSteps:\n1. Force scales with charges over distance squared, governing all electric pushes exactly.\n2. So the answer stands: Force scales with charges over distance squared, governing all electric pushes exactly."}
{"id": "phy_0027", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Teplota je 15 °C. Převeď ji na kelviny.", "choices": null, "answer": "Teplota: 288 K.", "steps": ["Přičti 273.", "15 + 273.", "= 288 K."], "text": "Answer: Teplota: 288 K.\nSteps:\n1. Přičti 273.\n2. 15 + 273.\n3. = 288 K."}
{"id": "phy_0028", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why refraction?", "choices": null, "answer": "Speed change at boundaries bends rays by Snell's law, shifting straws in water.", "steps": ["Speed change at boundaries bends rays by Snell's law, shifting straws in water.", "So the answer stands: Speed change at boundaries bends rays by Snell's law, shifting straws in water."], "text": "Answer: Speed change at boundaries bends rays by Snell's law, shifting straws in water.\nSteps:\n1. Speed change at boundaries bends rays by Snell's law, shifting straws in water.\n2. So the answer stands: Speed change at boundaries bends rays by Snell's law, shifting straws in water."}
{"id": "phy_0029", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 100 Hz and λ = 2 m. What is its speed?", "choices": {"A": "200 m/s", "B": "150 m/s", "C": "250 m/s", "D": "300 m/s"}, "answer": "Speed is 200 m/s.", "steps": ["v = 100 Hz × 2 m.", "v = 200 m/s.", "Select option A."], "text": "Answer: 200 m/s\nSteps:\n1. v = 100 Hz × 2 m.\n2. v = 200 m/s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0030", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is relativity?", "choices": null, "answer": "Motion warps time and space together, keeping light speed fixed for all.", "steps": ["Motion warps time and space together, keeping light speed fixed for all.", "So the answer stands: Motion warps time and space together, keeping light speed fixed for all."], "text": "Answer: Motion warps time and space together, keeping light speed fixed for all.\nSteps:\n1. Motion warps time and space together, keeping light speed fixed for all.\n2. So the answer stands: Motion warps time and space together, keeping light speed fixed for all."}
{"id": "phy_0031", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why F equals ma?", "choices": null, "answer": "Net force equals mass times acceleration, linking pushes to motion change exactly.", "steps": ["Net force equals mass times acceleration, linking pushes to motion change exactly.", "So the answer stands: Net force equals mass times acceleration, linking pushes to motion change exactly."], "text": "Answer: Net force equals mass times acceleration, linking pushes to motion change exactly.\nSteps:\n1. Net force equals mass times acceleration, linking pushes to motion change exactly.\n2. So the answer stands: Net force equals mass times acceleration, linking pushes to motion change exactly."}
{"id": "phy_0032", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Co je elektrický náboj?", "choices": null, "answer": "Náboj je zdrojem elektrické síly, opačné se přitahují.", "steps": ["Náboj je zdrojem elektrické síly, opačné se přitahují.", "Odpověď tedy platí: Náboj je zdrojem elektrické síly, opačné se přitahují."], "text": "Answer: Náboj je zdrojem elektrické síly, opačné se přitahují.\nSteps:\n1. Náboj je zdrojem elektrické síly, opačné se přitahují.\n2. Odpověď tedy platí: Náboj je zdrojem elektrické síly, opačné se přitahují."}
{"id": "phy_0033", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 16 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 289 K.", "steps": ["Add 273.", "16 + 273.", "= 289 K."], "text": "Answer: Temperature: 289 K.\nSteps:\n1. Add 273.\n2. 16 + 273.\n3. = 289 K."}
{"id": "phy_0034", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 30 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "15 cm", "B": "25 cm", "C": "20 cm", "D": "30 cm"}, "answer": "Apparent depth is 20 cm.", "steps": ["d' = 30 cm / 1.5.", "d' = 20 cm.", "Select option C."], "text": "Answer: 20 cm\nSteps:\n1. d' = 30 cm / 1.5.\n2. d' = 20 cm.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0035", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 2 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 680 m.", "steps": ["d = v×t.", "d = 340 m/s × 2 s.", "= 680 m."], "text": "Answer: Distance: 680 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 2 s.\n3. = 680 m."}
{"id": "phy_0036", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why time dilation?", "choices": null, "answer": "Moving clocks tick slower as seen from rest, confirmed by muons daily.", "steps": ["Moving clocks tick slower as seen from rest, confirmed by muons daily.", "So the answer stands: Moving clocks tick slower as seen from rest, confirmed by muons daily."], "text": "Answer: Moving clocks tick slower as seen from rest, confirmed by muons daily.\nSteps:\n1. Moving clocks tick slower as seen from rest, confirmed by muons daily.\n2. So the answer stands: Moving clocks tick slower as seen from rest, confirmed by muons daily."}
{"id": "phy_0037", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 10 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 40 J.", "steps": ["W = F×d.", "W = 10 N × 4 m.", "= 40 J."], "text": "Answer: Work: 40 J.\nSteps:\n1. W = F×d.\n2. W = 10 N × 4 m.\n3. = 40 J."}
{"id": "phy_0038", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 2 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 12 W.", "steps": ["P = I²×R.", "P = (2 A)² × 3 Ω.", "= 12 W."], "text": "Answer: Power: 12 W.\nSteps:\n1. P = I²×R.\n2. P = (2 A)² × 3 Ω.\n3. = 12 W."}
{"id": "phy_0039", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 20 °C. What is it in kelvin?", "choices": {"A": "293 K", "B": "292 K", "C": "294 K", "D": "295 K"}, "answer": "Temperature is 293 K.", "steps": ["20 °C + 273.", "= 293 K.", "Select option A."], "text": "Answer: 293 K\nSteps:\n1. 20 °C + 273.\n2. = 293 K.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0040", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 4×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 1.3 s.", "steps": ["t = d/c.", "t = 4×10⁸ / 3×10⁸ s.", "= 1.3 s."], "text": "Answer: Time: 1.3 s.\nSteps:\n1. t = d/c.\n2. t = 4×10⁸ / 3×10⁸ s.\n3. = 1.3 s."}
{"id": "phy_0041", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Základ struny je 100 Hz. Spočítej její 3. harmonickou.", "choices": null, "answer": "3. harmonická: 300 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 100 Hz.", "= 300 Hz."], "text": "Answer: 3. harmonická: 300 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 100 Hz.\n3. = 300 Hz."}
{"id": "phy_0042", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is length contraction?", "choices": null, "answer": "Fast objects shorten along motion as measured from rest frames.", "steps": ["Fast objects shorten along motion as measured from rest frames.", "So the answer stands: Fast objects shorten along motion as measured from rest frames."], "text": "Answer: Fast objects shorten along motion as measured from rest frames.\nSteps:\n1. Fast objects shorten along motion as measured from rest frames.\n2. So the answer stands: Fast objects shorten along motion as measured from rest frames."}
{"id": "phy_0043", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 100 m in 10 s. What is its speed?", "choices": {"A": "9 m/s", "B": "10 m/s", "C": "11 m/s", "D": "12 m/s"}, "answer": "Speed is 10 m/s.", "steps": ["v = 100 m / 10 s.", "v = 10 m/s.", "Select option B."], "text": "Answer: 10 m/s\nSteps:\n1. v = 100 m / 10 s.\n2. v = 10 m/s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0044", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 2 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 24 V.", "steps": ["V = I×R.", "V = 2 A × 12 Ω.", "= 24 V."], "text": "Answer: Voltage: 24 V.\nSteps:\n1. V = I×R.\n2. V = 2 A × 12 Ω.\n3. = 24 V."}
{"id": "phy_0045", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 2 K? (c = 4186 J/(kg·K))", "choices": {"A": "4186 J", "B": "8372 J", "C": "12558 J", "D": "16744 J"}, "answer": "Heat needed is 8372 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 2 K.", "Q = 8372 J.", "Select option B."], "text": "Answer: 8372 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 2 K.\n2. Q = 8372 J.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0046", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Obraz vzniká 30 cm od čočky, předmět v 10 cm. Spočítej zvětšení.", "choices": null, "answer": "Zvětšení: 3×.", "steps": ["M = di/do.", "M = 30 cm / 10 cm.", "= 3×."], "text": "Answer: Zvětšení: 3×.\nSteps:\n1. M = di/do.\n2. M = 30 cm / 10 cm.\n3. = 3×."}
{"id": "phy_0047", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Co je vlna?", "choices": null, "answer": "Vlny nesou energii kmitáním bez přenosu látky.", "steps": ["Vlny nesou energii kmitáním bez přenosu látky.", "Odpověď tedy platí: Vlny nesou energii kmitáním bez přenosu látky."], "text": "Answer: Vlny nesou energii kmitáním bez přenosu látky.\nSteps:\n1. Vlny nesou energii kmitáním bez přenosu látky.\n2. Odpověď tedy platí: Vlny nesou energii kmitáním bez přenosu látky."}
{"id": "phy_0048", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Atom je vybuzen do hladiny n = 4. Spočítej čáry, jež může vyzářit.", "choices": null, "answer": "Čar: 6.", "steps": ["Dvojice: 4×3/2.", "= 12/2.", "= 6."], "text": "Answer: Čar: 6.\nSteps:\n1. Dvojice: 4×3/2.\n2. = 12/2.\n3. = 6."}
{"id": "phy_0049", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Co je první Newtonův zákon?", "choices": null, "answer": "Tělesa drží rychlost bez výsledné síly.", "steps": ["Tělesa drží rychlost bez výsledné síly.", "Odpověď tedy platí: Tělesa drží rychlost bez výsledné síly."], "text": "Answer: Tělesa drží rychlost bez výsledné síly.\nSteps:\n1. Tělesa drží rychlost bez výsledné síly.\n2. Odpověď tedy platí: Tělesa drží rychlost bez výsledné síly."}
{"id": "phy_0050", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is an electric field?", "choices": null, "answer": "Fields map force per charge through space, picturing influence before charges arrive.", "steps": ["Fields map force per charge through space, picturing influence before charges arrive.", "So the answer stands: Fields map force per charge through space, picturing influence before charges arrive."], "text": "Answer: Fields map force per charge through space, picturing influence before charges arrive.\nSteps:\n1. Fields map force per charge through space, picturing influence before charges arrive.\n2. So the answer stands: Fields map force per charge through space, picturing influence before charges arrive."}
{"id": "phy_0051", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 2 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 16744 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 2 K.", "= 16744 J."], "text": "Answer: Heat: 16744 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 2 K.\n2. = 16744 J."}
{"id": "phy_0052", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is Snell's law?", "choices": null, "answer": "n₁sinθ₁ equals n₂sinθ₂, predicting bend amounts exactly at interfaces.", "steps": ["n₁sinθ₁ equals n₂sinθ₂, predicting bend amounts exactly at interfaces.", "So the answer stands: n₁sinθ₁ equals n₂sinθ₂, predicting bend amounts exactly at interfaces."], "text": "Answer: n₁sinθ₁ equals n₂sinθ₂, predicting bend amounts exactly at interfaces.\nSteps:\n1. n₁sinθ₁ equals n₂sinθ₂, predicting bend amounts exactly at interfaces.\n2. So the answer stands: n₁sinθ₁ equals n₂sinθ₂, predicting bend amounts exactly at interfaces."}
{"id": "phy_0053", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 100 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 300 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 100 Hz.", "= 300 Hz."], "text": "Answer: 3rd harmonic: 300 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 100 Hz.\n3. = 300 Hz."}
{"id": "phy_0054", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 2 protons and 2 neutrons. What is its mass number?", "choices": {"A": "3", "B": "5", "C": "4", "D": "6"}, "answer": "Mass number is 4.", "steps": ["A = 2 + 2.", "A = 4.", "Select option C."], "text": "Answer: 4\nSteps:\n1. A = 2 + 2.\n2. A = 4.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0055", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 4 m/s. What is its kinetic energy?", "choices": {"A": "12 J", "B": "20 J", "C": "16 J", "D": "24 J"}, "answer": "Kinetic energy is 16 J.", "steps": ["KE = ½×2 kg×(4 m/s)².", "KE = 16 J.", "Select option C."], "text": "Answer: 16 J\nSteps:\n1. KE = ½×2 kg×(4 m/s)².\n2. KE = 16 J.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0056", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 6 s. Compute the energy used.", "choices": null, "answer": "Energy: 600 J.", "steps": ["E = P×t.", "E = 100 W × 6 s.", "= 600 J."], "text": "Answer: Energy: 600 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 6 s.\n3. = 600 J."}
{"id": "phy_0057", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 600 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 60 W.", "steps": ["P = W/t.", "P = 600 J / 10 s.", "= 60 W."], "text": "Answer: Power: 60 W.\nSteps:\n1. P = W/t.\n2. P = 600 J / 10 s.\n3. = 60 W."}
{"id": "phy_0058", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Co je odraz?", "choices": null, "answer": "Světlo se odráží pod stejným úhlem.", "steps": ["Světlo se odráží pod stejným úhlem.", "Odpověď tedy platí: Světlo se odráží pod stejným úhlem."], "text": "Answer: Světlo se odráží pod stejným úhlem.\nSteps:\n1. Světlo se odráží pod stejným úhlem.\n2. Odpověď tedy platí: Světlo se odráží pod stejným úhlem."}
{"id": "phy_0059", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why wavelength?", "choices": null, "answer": "It is the length of one full cycle, linking speed and frequency.", "steps": ["It is the length of one full cycle, linking speed and frequency.", "So the answer stands: It is the length of one full cycle, linking speed and frequency."], "text": "Answer: It is the length of one full cycle, linking speed and frequency.\nSteps:\n1. It is the length of one full cycle, linking speed and frequency.\n2. So the answer stands: It is the length of one full cycle, linking speed and frequency."}
{"id": "phy_0060", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why E equals mc²?", "choices": null, "answer": "Mass is frozen energy convertible in nuclei and stars.", "steps": ["Mass is frozen energy convertible in nuclei and stars.", "So the answer stands: Mass is frozen energy convertible in nuclei and stars."], "text": "Answer: Mass is frozen energy convertible in nuclei and stars.\nSteps:\n1. Mass is frozen energy convertible in nuclei and stars.\n2. So the answer stands: Mass is frozen energy convertible in nuclei and stars."}
{"id": "phy_0061", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what keeps velocity?", "choices": {"A": "Big friction", "B": "Strong wind", "C": "Loud noise", "D": "Zero net force"}, "answer": "The answer is Zero net force.", "steps": ["First law rules.", "So: Zero net force.", "Select option D."], "text": "Answer: Zero net force\nSteps:\n1. First law rules.\n2. So: Zero net force.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0062", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 3 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 27 W.", "steps": ["P = I²×R.", "P = (3 A)² × 3 Ω.", "= 27 W."], "text": "Answer: Power: 27 W.\nSteps:\n1. P = I²×R.\n2. P = (3 A)² × 3 Ω.\n3. = 27 W."}
{"id": "phy_0063", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Pokojová teplota je 20 °C. Kolik je to kelvinů?", "choices": {"A": "293 K", "B": "292 K", "C": "294 K", "D": "295 K"}, "answer": "Teplota je 293 K.", "steps": ["20 °C + 273.", "= 293 K.", "Vyber možnost A."], "text": "Answer: 293 K\nSteps:\n1. 20 °C + 273.\n2. = 293 K.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0064", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Světlo letí 4×10⁸ m. Spočítej dobu letu. (c = 3×10⁸ m/s)", "choices": null, "answer": "Čas: 1,3 s.", "steps": ["t = d/c.", "t = 4×10⁸ / 3×10⁸ s.", "= 1,3 s."], "text": "Answer: Čas: 1,3 s.\nSteps:\n1. t = d/c.\n2. t = 4×10⁸ / 3×10⁸ s.\n3. = 1,3 s."}
{"id": "phy_0065", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 2 Hz. What is its period?", "choices": {"A": "0.33 s", "B": "0.5 s", "C": "0.25 s", "D": "1 s"}, "answer": "Period is 0.5 s.", "steps": ["T = 1 / 2 Hz.", "T = 0.5 s.", "Select option B."], "text": "Answer: 0.5 s\nSteps:\n1. T = 1 / 2 Hz.\n2. T = 0.5 s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0066", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 4. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 6.", "steps": ["Pairs: 4×3/2.", "= 12/2.", "= 6."], "text": "Answer: Lines: 6.\nSteps:\n1. Pairs: 4×3/2.\n2. = 12/2.\n3. = 6."}
{"id": "phy_0067", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what bends circles?", "choices": {"A": "Centripetal force", "B": "Friction", "C": "Weight", "D": "Buoyancy"}, "answer": "The answer is Centripetal force.", "steps": ["Inward net pulls.", "So: Centripetal force.", "Select option A."], "text": "Answer: Centripetal force\nSteps:\n1. Inward net pulls.\n2. So: Centripetal force.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0068", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 3 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 36 V.", "steps": ["V = I×R.", "V = 3 A × 12 Ω.", "= 36 V."], "text": "Answer: Voltage: 36 V.\nSteps:\n1. V = I×R.\n2. V = 3 A × 12 Ω.\n3. = 36 V."}
{"id": "phy_0069", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why Kelvin scale?", "choices": null, "answer": "Kelvin starts at absolute zero where motion stops, suiting gas laws exactly.", "steps": ["Kelvin starts at absolute zero where motion stops, suiting gas laws exactly.", "So the answer stands: Kelvin starts at absolute zero where motion stops, suiting gas laws exactly."], "text": "Answer: Kelvin starts at absolute zero where motion stops, suiting gas laws exactly.\nSteps:\n1. Kelvin starts at absolute zero where motion stops, suiting gas laws exactly.\n2. So the answer stands: Kelvin starts at absolute zero where motion stops, suiting gas laws exactly."}
{"id": "phy_0070", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 45 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 30 cm.", "steps": ["d' = d/n.", "d' = 45 cm / 1.5.", "= 30 cm."], "text": "Answer: Apparent depth: 30 cm.\nSteps:\n1. d' = d/n.\n2. d' = 45 cm / 1.5.\n3. = 30 cm."}
{"id": "phy_0071", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 110 Hz. What is its 3rd harmonic?", "choices": {"A": "300 Hz", "B": "360 Hz", "C": "330 Hz", "D": "390 Hz"}, "answer": "3rd harmonic is 330 Hz.", "steps": ["f3 = 3 × 110 Hz.", "f3 = 330 Hz.", "Select option C."], "text": "Answer: 330 Hz\nSteps:\n1. f3 = 3 × 110 Hz.\n2. f3 = 330 Hz.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0072", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 3 protons and 4 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 7.", "steps": ["A = Z+N.", "A = 3 + 4.", "= 7."], "text": "Answer: Mass number: 7.\nSteps:\n1. A = Z+N.\n2. A = 3 + 4.\n3. = 7."}
{"id": "phy_0073", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 5 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 15 kg·m/s.", "steps": ["p = m×v.", "p = 5 kg × 3 m/s.", "= 15 kg·m/s."], "text": "Answer: Momentum: 15 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 5 kg × 3 m/s.\n3. = 15 kg·m/s."}
{"id": "phy_0074", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 1 A teče přes 12 Ω. Spočítej napětí.", "choices": null, "answer": "Napětí: 12 V.", "steps": ["U = I×R.", "U = 1 A × 12 Ω.", "= 12 V."], "text": "Answer: Napětí: 12 V.\nSteps:\n1. U = I×R.\n2. U = 1 A × 12 Ω.\n3. = 12 V."}
{"id": "phy_0075", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is heat?", "choices": null, "answer": "Heat is energy flowing from hot to cold spontaneously, measured in joules.", "steps": ["Heat is energy flowing from hot to cold spontaneously, measured in joules.", "So the answer stands: Heat is energy flowing from hot to cold spontaneously, measured in joules."], "text": "Answer: Heat is energy flowing from hot to cold spontaneously, measured in joules.\nSteps:\n1. Heat is energy flowing from hot to cold spontaneously, measured in joules.\n2. So the answer stands: Heat is energy flowing from hot to cold spontaneously, measured in joules."}
{"id": "phy_0076", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what bounces equal?", "choices": {"A": "Refraction", "B": "Diffusion", "C": "Absorption", "D": "Reflection"}, "answer": "The answer is Reflection.", "steps": ["Angles matched.", "So: Reflection.", "Select option D."], "text": "Answer: Reflection\nSteps:\n1. Angles matched.\n2. So: Reflection.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0077", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 250 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 750 m/s.", "steps": ["v = f×λ.", "v = 250 Hz × 3 m.", "= 750 m/s."], "text": "Answer: Speed: 750 m/s.\nSteps:\n1. v = f×λ.\n2. v = 250 Hz × 3 m.\n3. = 750 m/s."}
{"id": "phy_0078", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 1600 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 400.", "steps": ["Halve: 1600 → 800.", "Halve: 800 → 400.", "= 400."], "text": "Answer: Survivors: 400.\nSteps:\n1. Halve: 1600 → 800.\n2. Halve: 800 → 400.\n3. = 400."}
{"id": "phy_0079", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Proč F rovno ma?", "choices": null, "answer": "Výsledná síla rovná se hmotnosti krát zrychlení.", "steps": ["Výsledná síla rovná se hmotnosti krát zrychlení.", "Odpověď tedy platí: Výsledná síla rovná se hmotnosti krát zrychlení."], "text": "Answer: Výsledná síla rovná se hmotnosti krát zrychlení.\nSteps:\n1. Výsledná síla rovná se hmotnosti krát zrychlení.\n2. Odpověď tedy platí: Výsledná síla rovná se hmotnosti krát zrychlení."}
{"id": "phy_0080", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why field lines?", "choices": null, "answer": "Lines show direction and crowding strength, making invisible forces visible neatly.", "steps": ["Lines show direction and crowding strength, making invisible forces visible neatly.", "So the answer stands: Lines show direction and crowding strength, making invisible forces visible neatly."], "text": "Answer: Lines show direction and crowding strength, making invisible forces visible neatly.\nSteps:\n1. Lines show direction and crowding strength, making invisible forces visible neatly.\n2. So the answer stands: Lines show direction and crowding strength, making invisible forces visible neatly."}
{"id": "phy_0081", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 200 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "10%", "B": "30%", "C": "20%", "D": "40%"}, "answer": "Efficiency is 20%.", "steps": ["200 J / 1000 J.", "= 20%.", "Select option C."], "text": "Answer: 20%\nSteps:\n1. 200 J / 1000 J.\n2. = 20%.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0082", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 40 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 4×.", "steps": ["M = di/do.", "M = 40 cm / 10 cm.", "= 4×."], "text": "Answer: Magnification: 4×.\nSteps:\n1. M = di/do.\n2. M = 40 cm / 10 cm.\n3. = 4×."}
{"id": "phy_0083", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 3 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 1020 m.", "steps": ["d = v×t.", "d = 340 m/s × 3 s.", "= 1020 m."], "text": "Answer: Distance: 1020 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 3 s.\n3. = 1020 m."}
{"id": "phy_0084", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 5. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 10.", "steps": ["Pairs: 5×4/2.", "= 20/2.", "= 10."], "text": "Answer: Lines: 10.\nSteps:\n1. Pairs: 5×4/2.\n2. = 20/2.\n3. = 10."}
{"id": "phy_0085", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 3 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "6 N", "B": "9 N", "C": "12 N", "D": "15 N"}, "answer": "Net force is 9 N.", "steps": ["F = 3 kg × 3 m/s².", "F = 9 N.", "Select option B."], "text": "Answer: 9 N\nSteps:\n1. F = 3 kg × 3 m/s².\n2. F = 9 N.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0086", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is voltage?", "choices": null, "answer": "Voltage is energy per charge in volts, pushing current through circuits.", "steps": ["Voltage is energy per charge in volts, pushing current through circuits.", "So the answer stands: Voltage is energy per charge in volts, pushing current through circuits."], "text": "Answer: Voltage is energy per charge in volts, pushing current through circuits.\nSteps:\n1. Voltage is energy per charge in volts, pushing current through circuits.\n2. So the answer stands: Voltage is energy per charge in volts, pushing current through circuits."}
{"id": "phy_0087", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why specific heat?", "choices": null, "answer": "It is energy per mass per degree, high for water that buffers climate.", "steps": ["It is energy per mass per degree, high for water that buffers climate.", "So the answer stands: It is energy per mass per degree, high for water that buffers climate."], "text": "Answer: It is energy per mass per degree, high for water that buffers climate.\nSteps:\n1. It is energy per mass per degree, high for water that buffers climate.\n2. So the answer stands: It is energy per mass per degree, high for water that buffers climate."}
{"id": "phy_0088", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what splits white?", "choices": {"A": "Prism", "B": "Mirror", "C": "Lens", "D": "Screen"}, "answer": "The answer is Prism.", "steps": ["Colours fanned.", "So: Prism.", "Select option A."], "text": "Answer: Prism\nSteps:\n1. Colours fanned.\n2. So: Prism.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0089", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vlna na struně má f = 100 Hz a λ = 2 m. Jaká je její rychlost?", "choices": {"A": "200 m/s", "B": "150 m/s", "C": "250 m/s", "D": "300 m/s"}, "answer": "Rychlost je 200 m/s.", "steps": ["v = 100 Hz × 2 m.", "v = 200 m/s.", "Vyber možnost A."], "text": "Answer: 200 m/s\nSteps:\n1. v = 100 Hz × 2 m.\n2. v = 200 m/s.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0090", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what warps together?", "choices": {"A": "Spacecraft", "B": "Timetable", "C": "Workbench", "D": "Spacetime"}, "answer": "The answer is Spacetime.", "steps": ["c fixed for all.", "So: Spacetime.", "Select option D."], "text": "Answer: Spacetime\nSteps:\n1. c fixed for all.\n2. So: Spacetime.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0091", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 4 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 8 N.", "steps": ["F = m×a.", "F = 4 kg × 2 m/s².", "= 8 N."], "text": "Answer: Net force: 8 N.\nSteps:\n1. F = m×a.\n2. F = 4 kg × 2 m/s².\n3. = 8 N."}
{"id": "phy_0092", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why Ohm's law?", "choices": null, "answer": "V equals IR for resistors, linking push, flow, and opposition simply.", "steps": ["V equals IR for resistors, linking push, flow, and opposition simply.", "So the answer stands: V equals IR for resistors, linking push, flow, and opposition simply."], "text": "Answer: V equals IR for resistors, linking push, flow, and opposition simply.\nSteps:\n1. V equals IR for resistors, linking push, flow, and opposition simply.\n2. So the answer stands: V equals IR for resistors, linking push, flow, and opposition simply."}
{"id": "phy_0093", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is thermal expansion?", "choices": null, "answer": "Heated particles spread apart, lengthening bridges and loosening lids.", "steps": ["Heated particles spread apart, lengthening bridges and loosening lids.", "So the answer stands: Heated particles spread apart, lengthening bridges and loosening lids."], "text": "Answer: Heated particles spread apart, lengthening bridges and loosening lids.\nSteps:\n1. Heated particles spread apart, lengthening bridges and loosening lids.\n2. So the answer stands: Heated particles spread apart, lengthening bridges and loosening lids."}
{"id": "phy_0094", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 7×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 2.3 s.", "steps": ["t = d/c.", "t = 7×10⁸ / 3×10⁸ s.", "= 2.3 s."], "text": "Answer: Time: 2.3 s.\nSteps:\n1. t = d/c.\n2. t = 7×10⁸ / 3×10⁸ s.\n3. = 2.3 s."}
{"id": "phy_0095", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Proč vlnová délka?", "choices": null, "answer": "Je délka jednoho cyklu.", "steps": ["Je délka jednoho cyklu.", "Odpověď tedy platí: Je délka jednoho cyklu."], "text": "Answer: Je délka jednoho cyklu.\nSteps:\n1. Je délka jednoho cyklu.\n2. Odpověď tedy platí: Je délka jednoho cyklu."}
{"id": "phy_0096", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is spacetime?", "choices": null, "answer": "Time joins space as one four-dimensional fabric curved by mass.", "steps": ["Time joins space as one four-dimensional fabric curved by mass.", "So the answer stands: Time joins space as one four-dimensional fabric curved by mass."], "text": "Answer: Time joins space as one four-dimensional fabric curved by mass.\nSteps:\n1. Time joins space as one four-dimensional fabric curved by mass.\n2. So the answer stands: Time joins space as one four-dimensional fabric curved by mass."}
{"id": "phy_0097", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is inertia?", "choices": null, "answer": "Inertia is mass resisting velocity change, so heavier objects need bigger forces to speed.", "steps": ["Inertia is mass resisting velocity change, so heavier objects need bigger forces to speed.", "So the answer stands: Inertia is mass resisting velocity change, so heavier objects need bigger forces to speed."], "text": "Answer: Inertia is mass resisting velocity change, so heavier objects need bigger forces to speed.\nSteps:\n1. Inertia is mass resisting velocity change, so heavier objects need bigger forces to speed.\n2. So the answer stands: Inertia is mass resisting velocity change, so heavier objects need bigger forces to speed."}
{"id": "phy_0098", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 7 s. Compute the energy used.", "choices": null, "answer": "Energy: 700 J.", "steps": ["E = P×t.", "E = 100 W × 7 s.", "= 700 J."], "text": "Answer: Energy: 700 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 7 s.\n3. = 700 J."}
{"id": "phy_0099", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what measures jiggle?", "choices": {"A": "Pressure", "B": "Volume", "C": "Mass", "D": "Temperature"}, "answer": "The answer is Temperature.", "steps": ["Mean energy read.", "So: Temperature.", "Select option D."], "text": "Answer: Temperature\nSteps:\n1. Mean energy read.\n2. So: Temperature.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0100", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why total internal reflection?", "choices": null, "answer": "Beyond the critical angle no transmission fits, so all light reflects inside gems.", "steps": ["Beyond the critical angle no transmission fits, so all light reflects inside gems.", "So the answer stands: Beyond the critical angle no transmission fits, so all light reflects inside gems."], "text": "Answer: Beyond the critical angle no transmission fits, so all light reflects inside gems.\nSteps:\n1. Beyond the critical angle no transmission fits, so all light reflects inside gems.\n2. So the answer stands: Beyond the critical angle no transmission fits, so all light reflects inside gems."}
{"id": "phy_0101", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 110 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 330 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 110 Hz.", "= 330 Hz."], "text": "Answer: 3rd harmonic: 330 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 110 Hz.\n3. = 330 Hz."}
{"id": "phy_0102", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 4 protons and 5 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 9.", "steps": ["A = Z+N.", "A = 4 + 5.", "= 9."], "text": "Answer: Mass number: 9.\nSteps:\n1. A = Z+N.\n2. A = 4 + 5.\n3. = 9."}
{"id": "phy_0103", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 15 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 60 J.", "steps": ["W = F×d.", "W = 15 N × 4 m.", "= 60 J."], "text": "Answer: Work: 60 J.\nSteps:\n1. W = F×d.\n2. W = 15 N × 4 m.\n3. = 60 J."}
{"id": "phy_0104", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 3 A. What is its power?", "choices": {"A": "24 W", "B": "36 W", "C": "48 W", "D": "60 W"}, "answer": "Power is 36 W.", "steps": ["P = 12 V × 3 A.", "P = 36 W.", "Select option B."], "text": "Answer: 36 W\nSteps:\n1. P = 12 V × 3 A.\n2. P = 36 W.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0105", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Kolik tepla ohřeje 2 kg vody o 1 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Teplo: 8372 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 1 K.", "= 8372 J."], "text": "Answer: Teplo: 8372 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 1 K.\n2. = 8372 J."}
{"id": "phy_0106", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 30 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "2×", "B": "3×", "C": "4×", "D": "5×"}, "answer": "Magnification is 3×.", "steps": ["M = 30 cm / 10 cm.", "M = 3×.", "Select option B."], "text": "Answer: 3×\nSteps:\n1. M = 30 cm / 10 cm.\n2. M = 3×.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0107", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what carries without matter?", "choices": {"A": "Wind", "B": "River", "C": "Truck", "D": "Wave"}, "answer": "The answer is Wave.", "steps": ["Energy travels.", "So: Wave.", "Select option D."], "text": "Answer: Wave\nSteps:\n1. Energy travels.\n2. So: Wave.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0108", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Co je relativita?", "choices": null, "answer": "Pohyb zakřivuje čas a prostor a drží c pevné.", "steps": ["Pohyb zakřivuje čas a prostor a drží c pevné.", "Odpověď tedy platí: Pohyb zakřivuje čas a prostor a drží c pevné."], "text": "Answer: Pohyb zakřivuje čas a prostor a drží c pevné.\nSteps:\n1. Pohyb zakřivuje čas a prostor a drží c pevné.\n2. Odpověď tedy platí: Pohyb zakřivuje čas a prostor a drží c pevné."}
{"id": "phy_0109", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 6 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 18 kg·m/s.", "steps": ["p = m×v.", "p = 6 kg × 3 m/s.", "= 18 kg·m/s."], "text": "Answer: Momentum: 18 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 6 kg × 3 m/s.\n3. = 18 kg·m/s."}
{"id": "phy_0110", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Proud 2 A teče přes 5 Ω. Jaké je napětí?", "choices": {"A": "10 V", "B": "5 V", "C": "15 V", "D": "20 V"}, "answer": "Napětí je 10 V.", "steps": ["U = 2 A × 5 Ω.", "U = 10 V.", "Vyber možnost A."], "text": "Answer: 10 V\nSteps:\n1. U = 2 A × 5 Ω.\n2. U = 10 V.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0111", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why conduction?", "choices": null, "answer": "Colliding particles pass energy along solids, fastest through metals.", "steps": ["Colliding particles pass energy along solids, fastest through metals.", "So the answer stands: Colliding particles pass energy along solids, fastest through metals."], "text": "Answer: Colliding particles pass energy along solids, fastest through metals.\nSteps:\n1. Colliding particles pass energy along solids, fastest through metals.\n2. So the answer stands: Colliding particles pass energy along solids, fastest through metals."}
{"id": "phy_0112", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 6×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "3 s", "B": "4 s", "C": "2 s", "D": "1 s"}, "answer": "Time is 2 s.", "steps": ["t = 6×10⁸ m / 3×10⁸ m/s.", "t = 2 s.", "Select option C."], "text": "Answer: 2 s\nSteps:\n1. t = 6×10⁸ m / 3×10⁸ m/s.\n2. t = 2 s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0113", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 300 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 900 m/s.", "steps": ["v = f×λ.", "v = 300 Hz × 3 m.", "= 900 m/s."], "text": "Answer: Speed: 900 m/s.\nSteps:\n1. v = f×λ.\n2. v = 300 Hz × 3 m.\n3. = 900 m/s."}
{"id": "phy_0114", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what splits heavy?", "choices": {"A": "Fission", "B": "Fusion", "C": "Fashion", "D": "Fiction"}, "answer": "The answer is Fission.", "steps": ["Reactors chained.", "So: Fission.", "Select option A."], "text": "Answer: Fission\nSteps:\n1. Reactors chained.\n2. So: Fission.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0115", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Auto ujede 100 m za 10 s. Jaká je jeho rychlost?", "choices": {"A": "9 m/s", "B": "10 m/s", "C": "11 m/s", "D": "12 m/s"}, "answer": "Rychlost je 10 m/s.", "steps": ["v = 100 m / 10 s.", "v = 10 m/s.", "Vyber možnost B."], "text": "Answer: 10 m/s\nSteps:\n1. v = 100 m / 10 s.\n2. v = 10 m/s.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0116", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 10 s. How much charge passes?", "choices": {"A": "20 C", "B": "60 C", "C": "40 C", "D": "80 C"}, "answer": "Charge is 40 C.", "steps": ["Q = 4 A × 10 s.", "Q = 40 C.", "Select option C."], "text": "Answer: 40 C\nSteps:\n1. Q = 4 A × 10 s.\n2. Q = 40 C.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0117", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is convection?", "choices": null, "answer": "Flowing fluids carry heat in currents, from radiators to weather.", "steps": ["Flowing fluids carry heat in currents, from radiators to weather.", "So the answer stands: Flowing fluids carry heat in currents, from radiators to weather."], "text": "Answer: Flowing fluids carry heat in currents, from radiators to weather.\nSteps:\n1. Flowing fluids carry heat in currents, from radiators to weather.\n2. So the answer stands: Flowing fluids carry heat in currents, from radiators to weather."}
{"id": "phy_0118", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 45 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "25 cm", "B": "35 cm", "C": "40 cm", "D": "30 cm"}, "answer": "Apparent depth is 30 cm.", "steps": ["d' = 45 cm / 1.5.", "d' = 30 cm.", "Select option D."], "text": "Answer: 30 cm\nSteps:\n1. d' = 45 cm / 1.5.\n2. d' = 30 cm.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0119", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 4 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 1360 m.", "steps": ["d = v×t.", "d = 340 m/s × 4 s.", "= 1360 m."], "text": "Answer: Distance: 1360 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 4 s.\n3. = 1360 m."}
{"id": "phy_0120", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why general relativity?", "choices": null, "answer": "Gravity is curved spacetime guiding falling paths, bending starlight.", "steps": ["Gravity is curved spacetime guiding falling paths, bending starlight.", "So the answer stands: Gravity is curved spacetime guiding falling paths, bending starlight."], "text": "Answer: Gravity is curved spacetime guiding falling paths, bending starlight.\nSteps:\n1. Gravity is curved spacetime guiding falling paths, bending starlight.\n2. So the answer stands: Gravity is curved spacetime guiding falling paths, bending starlight."}
{"id": "phy_0121", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Síla 10 N tlačí na dráze 4 m. Spočítej vykonanou práci.", "choices": null, "answer": "Práce: 40 J.", "steps": ["W = F×d.", "W = 10 N × 4 m.", "= 40 J."], "text": "Answer: Práce: 40 J.\nSteps:\n1. W = F×d.\n2. W = 10 N × 4 m.\n3. = 40 J."}
{"id": "phy_0122", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what attracts opposites?", "choices": {"A": "Mass", "B": "Spin", "C": "Color", "D": "Charge"}, "answer": "The answer is Charge.", "steps": ["Plus meets minus.", "So: Charge.", "Select option D."], "text": "Answer: Charge\nSteps:\n1. Plus meets minus.\n2. So: Charge.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0123", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 17 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 290 K.", "steps": ["Add 273.", "17 + 273.", "= 290 K."], "text": "Answer: Temperature: 290 K.\nSteps:\n1. Add 273.\n2. 17 + 273.\n3. = 290 K."}
{"id": "phy_0124", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Proč lom?", "choices": null, "answer": "Změna rychlosti ohýbá paprsky podle Snellova zákona.", "steps": ["Změna rychlosti ohýbá paprsky podle Snellova zákona.", "Odpověď tedy platí: Změna rychlosti ohýbá paprsky podle Snellova zákona."], "text": "Answer: Změna rychlosti ohýbá paprsky podle Snellova zákona.\nSteps:\n1. Změna rychlosti ohýbá paprsky podle Snellova zákona.\n2. Odpověď tedy platí: Změna rychlosti ohýbá paprsky podle Snellova zákona."}
{"id": "phy_0125", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Vlna na struně má f = 250 Hz a λ = 3 m. Spočítej její rychlost.", "choices": null, "answer": "Rychlost: 750 m/s.", "steps": ["v = f×λ.", "v = 250 Hz × 3 m.", "= 750 m/s."], "text": "Answer: Rychlost: 750 m/s.\nSteps:\n1. v = f×λ.\n2. v = 250 Hz × 3 m.\n3. = 750 m/s."}
{"id": "phy_0126", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 800 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "150", "B": "200", "C": "250", "D": "300"}, "answer": "200 atoms remain.", "steps": ["Halve twice: 800 → 400 → 200.", "Left: 200.", "Select option B."], "text": "Answer: 200\nSteps:\n1. Halve twice: 800 → 400 → 200.\n2. Left: 200.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0127", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 110 m in 10 s. What is its speed?", "choices": {"A": "10 m/s", "B": "12 m/s", "C": "11 m/s", "D": "13 m/s"}, "answer": "Speed is 11 m/s.", "steps": ["v = 110 m / 10 s.", "v = 11 m/s.", "Select option C."], "text": "Answer: 11 m/s\nSteps:\n1. v = 110 m / 10 s.\n2. v = 11 m/s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0128", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 4 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 48 W.", "steps": ["P = I²×R.", "P = (4 A)² × 3 Ω.", "= 48 W."], "text": "Answer: Power: 48 W.\nSteps:\n1. P = I²×R.\n2. P = (4 A)² × 3 Ω.\n3. = 48 W."}
{"id": "phy_0129", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Motor vykoná 500 J práce za 10 s. Spočítej jeho výkon.", "choices": null, "answer": "Výkon: 50 W.", "steps": ["P = W/t.", "P = 500 J / 10 s.", "= 50 W."], "text": "Answer: Výkon: 50 W.\nSteps:\n1. P = W/t.\n2. P = 500 J / 10 s.\n3. = 50 W."}
{"id": "phy_0130", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What are lenses for?", "choices": null, "answer": "Curved glass focuses rays to images, magnifying or projecting at will.", "steps": ["Curved glass focuses rays to images, magnifying or projecting at will.", "So the answer stands: Curved glass focuses rays to images, magnifying or projecting at will."], "text": "Answer: Curved glass focuses rays to images, magnifying or projecting at will.\nSteps:\n1. Curved glass focuses rays to images, magnifying or projecting at will.\n2. So the answer stands: Curved glass focuses rays to images, magnifying or projecting at will."}
{"id": "phy_0131", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 120 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 360 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 120 Hz.", "= 360 Hz."], "text": "Answer: 3rd harmonic: 360 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 120 Hz.\n3. = 360 Hz."}
{"id": "phy_0132", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is a black hole?", "choices": null, "answer": "Mass crushed inside its horizon traps even light forever.", "steps": ["Mass crushed inside its horizon traps even light forever.", "So the answer stands: Mass crushed inside its horizon traps even light forever."], "text": "Answer: Mass crushed inside its horizon traps even light forever.\nSteps:\n1. Mass crushed inside its horizon traps even light forever.\n2. So the answer stands: Mass crushed inside its horizon traps even light forever."}
{"id": "phy_0133", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 5 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 10 N.", "steps": ["F = m×a.", "F = 5 kg × 2 m/s².", "= 10 N."], "text": "Answer: Net force: 10 N.\nSteps:\n1. F = m×a.\n2. F = 5 kg × 2 m/s².\n3. = 10 N."}
{"id": "phy_0134", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Topidlo 100 W běží po 5 s. Spočítej spotřebovanou energii.", "choices": null, "answer": "Energie: 500 J.", "steps": ["E = P×t.", "E = 100 W × 5 s.", "= 500 J."], "text": "Answer: Energie: 500 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 5 s.\n3. = 500 J."}
{"id": "phy_0135", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 3 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 25116 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 3 K.", "= 25116 J."], "text": "Answer: Heat: 25116 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 3 K.\n2. = 25116 J."}
{"id": "phy_0136", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Předmět leží 45 cm hluboko ve skle (n = 1,5). Spočítej zdánlivou hloubku.", "choices": null, "answer": "Zdánlivá hloubka: 30 cm.", "steps": ["d' = d/n.", "d' = 45 cm / 1,5.", "= 30 cm."], "text": "Answer: Zdánlivá hloubka: 30 cm.\nSteps:\n1. d' = d/n.\n2. d' = 45 cm / 1,5.\n3. = 30 cm."}
{"id": "phy_0137", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what colours timbre?", "choices": {"A": "Harmonics", "B": "Statics", "C": "Noises", "D": "Silences"}, "answer": "The answer is Harmonics.", "steps": ["Overtones added.", "So: Harmonics.", "Select option A."], "text": "Answer: Harmonics\nSteps:\n1. Overtones added.\n2. So: Harmonics.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0138", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 2400 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 600.", "steps": ["Halve: 2400 → 1200.", "Halve: 1200 → 600.", "= 600."], "text": "Answer: Survivors: 600.\nSteps:\n1. Halve: 2400 → 1200.\n2. Halve: 1200 → 600.\n3. = 600."}
{"id": "phy_0139", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 20 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 80 J.", "steps": ["W = F×d.", "W = 20 N × 4 m.", "= 80 J."], "text": "Answer: Work: 80 J.\nSteps:\n1. W = F×d.\n2. W = 20 N × 4 m.\n3. = 80 J."}
{"id": "phy_0140", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 4 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 48 V.", "steps": ["V = I×R.", "V = 4 A × 12 Ω.", "= 48 V."], "text": "Answer: Voltage: 48 V.\nSteps:\n1. V = I×R.\n2. V = 4 A × 12 Ω.\n3. = 48 V."}
{"id": "phy_0141", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 700 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 70 W.", "steps": ["P = W/t.", "P = 700 J / 10 s.", "= 70 W."], "text": "Answer: Power: 70 W.\nSteps:\n1. P = W/t.\n2. P = 700 J / 10 s.\n3. = 70 W."}
{"id": "phy_0142", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Obraz vzniká 20 cm od čočky, předmět v 10 cm. Jaké je zvětšení?", "choices": {"A": "2×", "B": "1×", "C": "3×", "D": "4×"}, "answer": "Zvětšení je 2×.", "steps": ["M = 20 cm / 10 cm.", "M = 2×.", "Vyber možnost A."], "text": "Answer: 2×\nSteps:\n1. M = 20 cm / 10 cm.\n2. M = 2×.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0143", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 150 Hz and λ = 2 m. What is its speed?", "choices": {"A": "250 m/s", "B": "300 m/s", "C": "350 m/s", "D": "400 m/s"}, "answer": "Speed is 300 m/s.", "steps": ["v = 150 Hz × 2 m.", "v = 300 m/s.", "Select option B."], "text": "Answer: 300 m/s\nSteps:\n1. v = 150 Hz × 2 m.\n2. v = 300 m/s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0144", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why Hawking radiation?", "choices": null, "answer": "Quantum pairs at horizons leak energy, slowly evaporating holes.", "steps": ["Quantum pairs at horizons leak energy, slowly evaporating holes.", "So the answer stands: Quantum pairs at horizons leak energy, slowly evaporating holes."], "text": "Answer: Quantum pairs at horizons leak energy, slowly evaporating holes.\nSteps:\n1. Quantum pairs at horizons leak energy, slowly evaporating holes.\n2. So the answer stands: Quantum pairs at horizons leak energy, slowly evaporating holes."}
{"id": "phy_0145", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 5 m/s. What is its kinetic energy?", "choices": {"A": "20 J", "B": "30 J", "C": "35 J", "D": "25 J"}, "answer": "Kinetic energy is 25 J.", "steps": ["KE = ½×2 kg×(5 m/s)².", "KE = 25 J.", "Select option D."], "text": "Answer: 25 J\nSteps:\n1. KE = ½×2 kg×(5 m/s)².\n2. KE = 25 J.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0146", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is current?", "choices": null, "answer": "Current is charge flow per second in amperes, the bloodstream of circuits.", "steps": ["Current is charge flow per second in amperes, the bloodstream of circuits.", "So the answer stands: Current is charge flow per second in amperes, the bloodstream of circuits."], "text": "Answer: Current is charge flow per second in amperes, the bloodstream of circuits.\nSteps:\n1. Current is charge flow per second in amperes, the bloodstream of circuits.\n2. So the answer stands: Current is charge flow per second in amperes, the bloodstream of circuits."}
{"id": "phy_0147", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what never falls isolated?", "choices": {"A": "Entropy", "B": "Energy", "C": "Mass", "D": "Charge"}, "answer": "The answer is Entropy.", "steps": ["Second law rules.", "So: Entropy.", "Select option A."], "text": "Answer: Entropy\nSteps:\n1. Second law rules.\n2. So: Entropy.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0148", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 60 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 40 cm.", "steps": ["d' = d/n.", "d' = 60 cm / 1.5.", "= 40 cm."], "text": "Answer: Apparent depth: 40 cm.\nSteps:\n1. d' = d/n.\n2. d' = 60 cm / 1.5.\n3. = 40 cm."}
{"id": "phy_0149", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 350 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1050 m/s.", "steps": ["v = f×λ.", "v = 350 Hz × 3 m.", "= 1050 m/s."], "text": "Answer: Speed: 1050 m/s.\nSteps:\n1. v = f×λ.\n2. v = 350 Hz × 3 m.\n3. = 1050 m/s."}
{"id": "phy_0150", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 6. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 15.", "steps": ["Pairs: 6×5/2.", "= 30/2.", "= 15."], "text": "Answer: Lines: 15.\nSteps:\n1. Pairs: 6×5/2.\n2. = 30/2.\n3. = 15."}
{"id": "phy_0151", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Co je setrvačnost?", "choices": null, "answer": "Setrvačnost je odpor hmotnosti vůči změně rychlosti.", "steps": ["Setrvačnost je odpor hmotnosti vůči změně rychlosti.", "Odpověď tedy platí: Setrvačnost je odpor hmotnosti vůči změně rychlosti."], "text": "Answer: Setrvačnost je odpor hmotnosti vůči změně rychlosti.\nSteps:\n1. Setrvačnost je odpor hmotnosti vůči změně rychlosti.\n2. Odpověď tedy platí: Setrvačnost je odpor hmotnosti vůči změně rychlosti."}
{"id": "phy_0152", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 8 s. Compute the energy used.", "choices": null, "answer": "Energy: 800 J.", "steps": ["E = P×t.", "E = 100 W × 8 s.", "= 800 J."], "text": "Answer: Energy: 800 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 8 s.\n3. = 800 J."}
{"id": "phy_0153", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why radiation?", "choices": null, "answer": "All objects emit photons by temperature, warming across empty space.", "steps": ["All objects emit photons by temperature, warming across empty space.", "So the answer stands: All objects emit photons by temperature, warming across empty space."], "text": "Answer: All objects emit photons by temperature, warming across empty space.\nSteps:\n1. All objects emit photons by temperature, warming across empty space.\n2. So the answer stands: All objects emit photons by temperature, warming across empty space."}
{"id": "phy_0154", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why focal length?", "choices": null, "answer": "It marks where parallel rays meet, setting lens power in diopters.", "steps": ["It marks where parallel rays meet, setting lens power in diopters.", "So the answer stands: It marks where parallel rays meet, setting lens power in diopters."], "text": "Answer: It marks where parallel rays meet, setting lens power in diopters.\nSteps:\n1. It marks where parallel rays meet, setting lens power in diopters.\n2. So the answer stands: It marks where parallel rays meet, setting lens power in diopters."}
{"id": "phy_0155", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is frequency?", "choices": null, "answer": "Cycles per second in hertz, setting pitch and colour.", "steps": ["Cycles per second in hertz, setting pitch and colour.", "So the answer stands: Cycles per second in hertz, setting pitch and colour."], "text": "Answer: Cycles per second in hertz, setting pitch and colour.\nSteps:\n1. Cycles per second in hertz, setting pitch and colour.\n2. So the answer stands: Cycles per second in hertz, setting pitch and colour."}
{"id": "phy_0156", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Proč dilatace času?", "choices": null, "answer": "Pohybující se hodiny tikají pomaleji.", "steps": ["Pohybující se hodiny tikají pomaleji.", "Odpověď tedy platí: Pohybující se hodiny tikají pomaleji."], "text": "Answer: Pohybující se hodiny tikají pomaleji.\nSteps:\n1. Pohybující se hodiny tikají pomaleji.\n2. Odpověď tedy platí: Pohybující se hodiny tikají pomaleji."}
{"id": "phy_0157", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 7 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 21 kg·m/s.", "steps": ["p = m×v.", "p = 7 kg × 3 m/s.", "= 21 kg·m/s."], "text": "Answer: Momentum: 21 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 7 kg × 3 m/s.\n3. = 21 kg·m/s."}
{"id": "phy_0158", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 5 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 75 W.", "steps": ["P = I²×R.", "P = (5 A)² × 3 Ω.", "= 75 W."], "text": "Answer: Power: 75 W.\nSteps:\n1. P = I²×R.\n2. P = (5 A)² × 3 Ω.\n3. = 75 W."}
{"id": "phy_0159", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 18 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 291 K.", "steps": ["Add 273.", "18 + 273.", "= 291 K."], "text": "Answer: Temperature: 291 K.\nSteps:\n1. Add 273.\n2. 18 + 273.\n3. = 291 K."}
{"id": "phy_0160", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Světlo letí 3×10⁸ m. Kolik sekund to trvá? (c = 3×10⁸ m/s)", "choices": {"A": "2 s", "B": "1 s", "C": "3 s", "D": "0.5 s"}, "answer": "Čas je 1 s.", "steps": ["t = 3×10⁸ m / 3×10⁸ m/s.", "t = 1 s.", "Vyber možnost B."], "text": "Answer: 1 s\nSteps:\n1. t = 3×10⁸ m / 3×10⁸ m/s.\n2. t = 1 s.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0161", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 5 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 1700 m.", "steps": ["d = v×t.", "d = 340 m/s × 5 s.", "= 1700 m."], "text": "Answer: Distance: 1700 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 5 s.\n3. = 1700 m."}
{"id": "phy_0162", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is the Big Bang?", "choices": null, "answer": "Space expanded from a hot dense state 13.8 billion years ago.", "steps": ["Space expanded from a hot dense state 13.8 billion years ago.", "So the answer stands: Space expanded from a hot dense state 13.8 billion years ago."], "text": "Answer: Space expanded from a hot dense state 13.8 billion years ago.\nSteps:\n1. Space expanded from a hot dense state 13.8 billion years ago.\n2. So the answer stands: Space expanded from a hot dense state 13.8 billion years ago."}
{"id": "phy_0163", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Míč 2 kg letí 4 m/s. Jaká je jeho kinetická energie?", "choices": {"A": "12 J", "B": "20 J", "C": "16 J", "D": "24 J"}, "answer": "Kinetická energie je 16 J.", "steps": ["KE = ½×2 kg×(4 m/s)².", "KE = 16 J.", "Vyber možnost C."], "text": "Answer: 16 J\nSteps:\n1. KE = ½×2 kg×(4 m/s)².\n2. KE = 16 J.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0164", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what drives coils?", "choices": {"A": "Changing flux", "B": "Steady heat", "C": "Calm air", "D": "Dark room"}, "answer": "The answer is Changing flux.", "steps": ["Induction rules.", "So: Changing flux.", "Select option A."], "text": "Answer: Changing flux\nSteps:\n1. Induction rules.\n2. So: Changing flux.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0165", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 21 °C. What is it in kelvin?", "choices": {"A": "293 K", "B": "294 K", "C": "295 K", "D": "296 K"}, "answer": "Temperature is 294 K.", "steps": ["21 °C + 273.", "= 294 K.", "Select option B."], "text": "Answer: 294 K\nSteps:\n1. 21 °C + 273.\n2. = 294 K.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0166", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is magnification?", "choices": null, "answer": "Image size over object size, greater than one in microscopes.", "steps": ["Image size over object size, greater than one in microscopes.", "So the answer stands: Image size over object size, greater than one in microscopes."], "text": "Answer: Image size over object size, greater than one in microscopes.\nSteps:\n1. Image size over object size, greater than one in microscopes.\n2. So the answer stands: Image size over object size, greater than one in microscopes."}
{"id": "phy_0167", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 3 Hz. What is its period?", "choices": {"A": "0.25 s", "B": "0.2 s", "C": "0.33 s", "D": "0.5 s"}, "answer": "Period is 0.33 s.", "steps": ["T = 1 / 3 Hz.", "T = 0.33 s.", "Select option C."], "text": "Answer: 0.33 s\nSteps:\n1. T = 1 / 3 Hz.\n2. T = 0.33 s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0168", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Jádro má 3 protonů a 4 neutronů. Spočítej jeho nukleonové číslo.", "choices": null, "answer": "Nukleonové číslo: 7.", "steps": ["A = Z+N.", "A = 3 + 4.", "= 7."], "text": "Answer: Nukleonové číslo: 7.\nSteps:\n1. A = Z+N.\n2. A = 3 + 4.\n3. = 7."}
{"id": "phy_0169", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 5 kg se pohybuje 3 m/s. Spočítej jeho hybnost.", "choices": null, "answer": "Hybnost: 15 kg·m/s.", "steps": ["p = m×v.", "p = 5 kg × 3 m/s.", "= 15 kg·m/s."], "text": "Answer: Hybnost: 15 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 5 kg × 3 m/s.\n3. = 15 kg·m/s."}
{"id": "phy_0170", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 3 A flows through 5 Ω. What is the voltage?", "choices": {"A": "10 V", "B": "15 V", "C": "20 V", "D": "25 V"}, "answer": "Voltage is 15 V.", "steps": ["V = 3 A × 5 Ω.", "V = 15 V.", "Select option B."], "text": "Answer: 15 V\nSteps:\n1. V = 3 A × 5 Ω.\n2. V = 15 V.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0171", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is the first law?", "choices": null, "answer": "Energy conservation for heat and work: added heat splits into work and internal gain.", "steps": ["Energy conservation for heat and work: added heat splits into work and internal gain.", "So the answer stands: Energy conservation for heat and work: added heat splits into work and internal gain."], "text": "Answer: Energy conservation for heat and work: added heat splits into work and internal gain.\nSteps:\n1. Energy conservation for heat and work: added heat splits into work and internal gain.\n2. So the answer stands: Energy conservation for heat and work: added heat splits into work and internal gain."}
{"id": "phy_0172", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 50 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 5×.", "steps": ["M = di/do.", "M = 50 cm / 10 cm.", "= 5×."], "text": "Answer: Magnification: 5×.\nSteps:\n1. M = di/do.\n2. M = 50 cm / 10 cm.\n3. = 5×."}
{"id": "phy_0173", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Hrom je slyšet 3 s po blesku. Jak daleko je bouře? (v = 340 m/s)", "choices": null, "answer": "Vzdálenost: 1020 m.", "steps": ["d = v×t.", "d = 340 m/s × 3 s.", "= 1020 m."], "text": "Answer: Vzdálenost: 1020 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 3 s.\n3. = 1020 m."}
{"id": "phy_0174", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why cosmic expansion?", "choices": null, "answer": "Distant galaxies recede faster with distance, stretching light red.", "steps": ["Distant galaxies recede faster with distance, stretching light red.", "So the answer stands: Distant galaxies recede faster with distance, stretching light red."], "text": "Answer: Distant galaxies recede faster with distance, stretching light red.\nSteps:\n1. Distant galaxies recede faster with distance, stretching light red.\n2. So the answer stands: Distant galaxies recede faster with distance, stretching light red."}
{"id": "phy_0175", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Proč akce-reakce?", "choices": null, "answer": "Každá síla má stejně velkého opačného partnera.", "steps": ["Každá síla má stejně velkého opačného partnera.", "Odpověď tedy platí: Každá síla má stejně velkého opačného partnera."], "text": "Answer: Každá síla má stejně velkého opačného partnera.\nSteps:\n1. Každá síla má stejně velkého opačného partnera.\n2. Odpověď tedy platí: Každá síla má stejně velkého opačného partnera."}
{"id": "phy_0176", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why resistance?", "choices": null, "answer": "Collisions inside conductors oppose drift, turning electric energy into heat.", "steps": ["Collisions inside conductors oppose drift, turning electric energy into heat.", "So the answer stands: Collisions inside conductors oppose drift, turning electric energy into heat."], "text": "Answer: Collisions inside conductors oppose drift, turning electric energy into heat.\nSteps:\n1. Collisions inside conductors oppose drift, turning electric energy into heat.\n2. So the answer stands: Collisions inside conductors oppose drift, turning electric energy into heat."}
{"id": "phy_0177", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why internal energy?", "choices": null, "answer": "It sums microscopic kinetic and potential stores, the hidden ledger of heat.", "steps": ["It sums microscopic kinetic and potential stores, the hidden ledger of heat.", "So the answer stands: It sums microscopic kinetic and potential stores, the hidden ledger of heat."], "text": "Answer: It sums microscopic kinetic and potential stores, the hidden ledger of heat.\nSteps:\n1. It sums microscopic kinetic and potential stores, the hidden ledger of heat.\n2. So the answer stands: It sums microscopic kinetic and potential stores, the hidden ledger of heat."}
{"id": "phy_0178", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why lens equation?", "choices": null, "answer": "1/f equals 1/do + 1/di, locating every image from object spots.", "steps": ["1/f equals 1/do + 1/di, locating every image from object spots.", "So the answer stands: 1/f equals 1/do + 1/di, locating every image from object spots."], "text": "Answer: 1/f equals 1/do + 1/di, locating every image from object spots.\nSteps:\n1. 1/f equals 1/do + 1/di, locating every image from object spots.\n2. So the answer stands: 1/f equals 1/do + 1/di, locating every image from object spots."}
{"id": "phy_0179", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 130 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 390 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 130 Hz.", "= 390 Hz."], "text": "Answer: 3rd harmonic: 390 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 130 Hz.\n3. = 390 Hz."}
{"id": "phy_0180", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Vzorek 1600 atomů projde 2 poločasy. Spočítej přeživší.", "choices": null, "answer": "Přeživší: 400.", "steps": ["Půl: 1600 → 800.", "Půl: 800 → 400.", "= 400."], "text": "Answer: Přeživší: 400.\nSteps:\n1. Půl: 1600 → 800.\n2. Půl: 800 → 400.\n3. = 400."}
{"id": "phy_0181", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 6 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 12 N.", "steps": ["F = m×a.", "F = 6 kg × 2 m/s².", "= 12 N."], "text": "Answer: Net force: 12 N.\nSteps:\n1. F = m×a.\n2. F = 6 kg × 2 m/s².\n3. = 12 N."}
{"id": "phy_0182", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 4 A. What is its power?", "choices": {"A": "36 W", "B": "60 W", "C": "48 W", "D": "72 W"}, "answer": "Power is 48 W.", "steps": ["P = 12 V × 4 A.", "P = 48 W.", "Select option C."], "text": "Answer: 48 W\nSteps:\n1. P = 12 V × 4 A.\n2. P = 48 W.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0183", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 3 K? (c = 4186 J/(kg·K))", "choices": {"A": "8372 J", "B": "16744 J", "C": "12558 J", "D": "20930 J"}, "answer": "Heat needed is 12558 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 3 K.", "Q = 12558 J.", "Select option C."], "text": "Answer: 12558 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 3 K.\n2. Q = 12558 J.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0184", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 10×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 3.3 s.", "steps": ["t = d/c.", "t = 10×10⁸ / 3×10⁸ s.", "= 3.3 s."], "text": "Answer: Time: 3.3 s.\nSteps:\n1. t = d/c.\n2. t = 10×10⁸ / 3×10⁸ s.\n3. = 3.3 s."}
{"id": "phy_0185", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 400 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1200 m/s.", "steps": ["v = f×λ.", "v = 400 Hz × 3 m.", "= 1200 m/s."], "text": "Answer: Speed: 1200 m/s.\nSteps:\n1. v = f×λ.\n2. v = 400 Hz × 3 m.\n3. = 1200 m/s."}
{"id": "phy_0186", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 5 protons and 6 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 11.", "steps": ["A = Z+N.", "A = 5 + 6.", "= 11."], "text": "Answer: Mass number: 11.\nSteps:\n1. A = Z+N.\n2. A = 5 + 6.\n3. = 11."}
{"id": "phy_0187", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why action-reaction?", "choices": null, "answer": "Every force has an equal opposite partner on the other body, conserving momentum always.", "steps": ["Every force has an equal opposite partner on the other body, conserving momentum always.", "So the answer stands: Every force has an equal opposite partner on the other body, conserving momentum always."], "text": "Answer: Every force has an equal opposite partner on the other body, conserving momentum always.\nSteps:\n1. Every force has an equal opposite partner on the other body, conserving momentum always.\n2. So the answer stands: Every force has an equal opposite partner on the other body, conserving momentum always."}
{"id": "phy_0188", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 5 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 60 V.", "steps": ["V = I×R.", "V = 5 A × 12 Ω.", "= 60 V."], "text": "Answer: Voltage: 60 V.\nSteps:\n1. V = I×R.\n2. V = 5 A × 12 Ω.\n3. = 60 V."}
{"id": "phy_0189", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 4 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 33488 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 4 K.", "= 33488 J."], "text": "Answer: Heat: 33488 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 4 K.\n2. = 33488 J."}
{"id": "phy_0190", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is a real image?", "choices": null, "answer": "Rays truly meet there, so screens catch it, unlike virtual mirages.", "steps": ["Rays truly meet there, so screens catch it, unlike virtual mirages.", "So the answer stands: Rays truly meet there, so screens catch it, unlike virtual mirages."], "text": "Answer: Rays truly meet there, so screens catch it, unlike virtual mirages.\nSteps:\n1. Rays truly meet there, so screens catch it, unlike virtual mirages.\n2. So the answer stands: Rays truly meet there, so screens catch it, unlike virtual mirages."}
{"id": "phy_0191", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why v equals fλ?", "choices": null, "answer": "Speed equals cycles times length, the master wave relation.", "steps": ["Speed equals cycles times length, the master wave relation.", "So the answer stands: Speed equals cycles times length, the master wave relation."], "text": "Answer: Speed equals cycles times length, the master wave relation.\nSteps:\n1. Speed equals cycles times length, the master wave relation.\n2. So the answer stands: Speed equals cycles times length, the master wave relation."}
{"id": "phy_0192", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 3200 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 800.", "steps": ["Halve: 3200 → 1600.", "Halve: 1600 → 800.", "= 800."], "text": "Answer: Survivors: 800.\nSteps:\n1. Halve: 3200 → 1600.\n2. Halve: 1600 → 800.\n3. = 800."}
{"id": "phy_0193", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what links push, motion?", "choices": {"A": "F equals ma", "B": "E equals mc", "C": "V equals IR", "D": "pV equals nRT"}, "answer": "The answer is F equals ma.", "steps": ["Second law binds.", "So: F equals ma.", "Select option A."], "text": "Answer: F equals ma\nSteps:\n1. Second law binds.\n2. So: F equals ma.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0194", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 9 s. Compute the energy used.", "choices": null, "answer": "Energy: 900 J.", "steps": ["E = P×t.", "E = 100 W × 9 s.", "= 900 J."], "text": "Answer: Energy: 900 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 9 s.\n3. = 900 J."}
{"id": "phy_0195", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 800 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 80 W.", "steps": ["P = W/t.", "P = 800 J / 10 s.", "= 80 W."], "text": "Answer: Power: 80 W.\nSteps:\n1. P = W/t.\n2. P = 800 J / 10 s.\n3. = 80 W."}
{"id": "phy_0196", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what bends at boundaries?", "choices": {"A": "Refraction", "B": "Reflection", "C": "Ejection", "D": "Injection"}, "answer": "The answer is Refraction.", "steps": ["Speeds differ.", "So: Refraction.", "Select option A."], "text": "Answer: Refraction\nSteps:\n1. Speeds differ.\n2. So: Refraction.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0197", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vlna má frekvenci 2 Hz. Jaká je její perioda?", "choices": {"A": "0,33 s", "B": "0,5 s", "C": "0,25 s", "D": "1 s"}, "answer": "Perioda je 0,5 s.", "steps": ["T = 1 / 2 Hz.", "T = 0,5 s.", "Vyber možnost B."], "text": "Answer: 0,5 s\nSteps:\n1. T = 1 / 2 Hz.\n2. T = 0,5 s.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0198", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Atom je vybuzen do hladiny n = 5. Spočítej čáry, jež může vyzářit.", "choices": null, "answer": "Čar: 10.", "steps": ["Dvojice: 5×4/2.", "= 20/2.", "= 10."], "text": "Answer: Čar: 10.\nSteps:\n1. Dvojice: 5×4/2.\n2. = 20/2.\n3. = 10."}
{"id": "phy_0199", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Co je tření?", "choices": null, "answer": "Tření brání klouzání a mění pohyb v teplo.", "steps": ["Tření brání klouzání a mění pohyb v teplo.", "Odpověď tedy platí: Tření brání klouzání a mění pohyb v teplo."], "text": "Answer: Tření brání klouzání a mění pohyb v teplo.\nSteps:\n1. Tření brání klouzání a mění pohyb v teplo.\n2. Odpověď tedy platí: Tření brání klouzání a mění pohyb v teplo."}
{"id": "phy_0200", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is electric power?", "choices": null, "answer": "Power VI in watts rates energy delivery, sizing bulbs and bills.", "steps": ["Power VI in watts rates energy delivery, sizing bulbs and bills.", "So the answer stands: Power VI in watts rates energy delivery, sizing bulbs and bills."], "text": "Answer: Power VI in watts rates energy delivery, sizing bulbs and bills.\nSteps:\n1. Power VI in watts rates energy delivery, sizing bulbs and bills.\n2. So the answer stands: Power VI in watts rates energy delivery, sizing bulbs and bills."}
{"id": "phy_0201", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 300 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "20%", "B": "40%", "C": "50%", "D": "30%"}, "answer": "Efficiency is 30%.", "steps": ["300 J / 1000 J.", "= 30%.", "Select option D."], "text": "Answer: 30%\nSteps:\n1. 300 J / 1000 J.\n2. = 30%.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0202", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why virtual images?", "choices": null, "answer": "Diverging rays seem to meet behind mirrors, so eyes see unreachable pictures.", "steps": ["Diverging rays seem to meet behind mirrors, so eyes see unreachable pictures.", "So the answer stands: Diverging rays seem to meet behind mirrors, so eyes see unreachable pictures."], "text": "Answer: Diverging rays seem to meet behind mirrors, so eyes see unreachable pictures.\nSteps:\n1. Diverging rays seem to meet behind mirrors, so eyes see unreachable pictures.\n2. So the answer stands: Diverging rays seem to meet behind mirrors, so eyes see unreachable pictures."}
{"id": "phy_0203", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is amplitude?", "choices": null, "answer": "Peak displacement from rest, setting loudness and brightness.", "steps": ["Peak displacement from rest, setting loudness and brightness.", "So the answer stands: Peak displacement from rest, setting loudness and brightness."], "text": "Answer: Peak displacement from rest, setting loudness and brightness.\nSteps:\n1. Peak displacement from rest, setting loudness and brightness.\n2. So the answer stands: Peak displacement from rest, setting loudness and brightness."}
{"id": "phy_0204", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is dark matter?", "choices": null, "answer": "Unseen mass bends galaxies more than visible stuff allows.", "steps": ["Unseen mass bends galaxies more than visible stuff allows.", "So the answer stands: Unseen mass bends galaxies more than visible stuff allows."], "text": "Answer: Unseen mass bends galaxies more than visible stuff allows.\nSteps:\n1. Unseen mass bends galaxies more than visible stuff allows.\n2. So the answer stands: Unseen mass bends galaxies more than visible stuff allows."}
{"id": "phy_0205", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 25 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 100 J.", "steps": ["W = F×d.", "W = 25 N × 4 m.", "= 100 J."], "text": "Answer: Work: 100 J.\nSteps:\n1. W = F×d.\n2. W = 25 N × 4 m.\n3. = 100 J."}
{"id": "phy_0206", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Žárovka běží na 12 V a bere 3 A. Jaký je její příkon?", "choices": {"A": "24 W", "B": "36 W", "C": "48 W", "D": "60 W"}, "answer": "Příkon je 36 W.", "steps": ["P = 12 V × 3 A.", "P = 36 W.", "Vyber možnost B."], "text": "Answer: 36 W\nSteps:\n1. P = 12 V × 3 A.\n2. P = 36 W.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0207", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 19 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 292 K.", "steps": ["Add 273.", "19 + 273.", "= 292 K."], "text": "Answer: Temperature: 292 K.\nSteps:\n1. Add 273.\n2. 19 + 273.\n3. = 292 K."}
{"id": "phy_0208", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 75 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 50 cm.", "steps": ["d' = d/n.", "d' = 75 cm / 1.5.", "= 50 cm."], "text": "Answer: Apparent depth: 50 cm.\nSteps:\n1. d' = d/n.\n2. d' = 75 cm / 1.5.\n3. = 50 cm."}
{"id": "phy_0209", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why period?", "choices": null, "answer": "It is seconds per cycle, the inverse of frequency always.", "steps": ["It is seconds per cycle, the inverse of frequency always.", "So the answer stands: It is seconds per cycle, the inverse of frequency always."], "text": "Answer: It is seconds per cycle, the inverse of frequency always.\nSteps:\n1. It is seconds per cycle, the inverse of frequency always.\n2. So the answer stands: It is seconds per cycle, the inverse of frequency always."}
{"id": "phy_0210", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why dark energy?", "choices": null, "answer": "Expansion accelerates as if vacuum pushes space apart.", "steps": ["Expansion accelerates as if vacuum pushes space apart.", "So the answer stands: Expansion accelerates as if vacuum pushes space apart."], "text": "Answer: Expansion accelerates as if vacuum pushes space apart.\nSteps:\n1. Expansion accelerates as if vacuum pushes space apart.\n2. So the answer stands: Expansion accelerates as if vacuum pushes space apart."}
{"id": "phy_0211", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 8 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 24 kg·m/s.", "steps": ["p = m×v.", "p = 8 kg × 3 m/s.", "= 24 kg·m/s."], "text": "Answer: Momentum: 24 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 8 kg × 3 m/s.\n3. = 24 kg·m/s."}
{"id": "phy_0212", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 15 s. How much charge passes?", "choices": {"A": "40 C", "B": "80 C", "C": "100 C", "D": "60 C"}, "answer": "Charge is 60 C.", "steps": ["Q = 4 A × 15 s.", "Q = 60 C.", "Select option D."], "text": "Answer: 60 C\nSteps:\n1. Q = 4 A × 15 s.\n2. Q = 60 C.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0213", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what starts at zero motion?", "choices": {"A": "Kelvin scale", "B": "Celsius scale", "C": "Beaufort scale", "D": "Richter scale"}, "answer": "The answer is Kelvin scale.", "steps": ["Absolute zero based.", "So: Kelvin scale.", "Select option A."], "text": "Answer: Kelvin scale\nSteps:\n1. Absolute zero based.\n2. So: Kelvin scale.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0214", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what proves waves?", "choices": {"A": "Reflection", "B": "Diffraction", "C": "Absorption", "D": "Emission"}, "answer": "The answer is Diffraction.", "steps": ["Edges fringed.", "So: Diffraction.", "Select option B."], "text": "Answer: Diffraction\nSteps:\n1. Edges fringed.\n2. So: Diffraction.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0215", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Základ struny je 110 Hz. Jaká je její 3. harmonická?", "choices": {"A": "300 Hz", "B": "360 Hz", "C": "330 Hz", "D": "390 Hz"}, "answer": "3. harmonická je 330 Hz.", "steps": ["f3 = 3 × 110 Hz.", "f3 = 330 Hz.", "Vyber možnost C."], "text": "Answer: 330 Hz\nSteps:\n1. f3 = 3 × 110 Hz.\n2. f3 = 330 Hz.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0216", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 4. How many spectral lines can it emit?", "choices": {"A": "5", "B": "7", "C": "6", "D": "8"}, "answer": "Count: 6.", "steps": ["Pairs: 4×3/2.", "Lines: 6.", "Select option C."], "text": "Answer: 6\nSteps:\n1. Pairs: 4×3/2.\n2. Lines: 6.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0217", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is friction?", "choices": null, "answer": "Friction opposes sliding between surfaces, converting motion energy into heat.", "steps": ["Friction opposes sliding between surfaces, converting motion energy into heat.", "So the answer stands: Friction opposes sliding between surfaces, converting motion energy into heat."], "text": "Answer: Friction opposes sliding between surfaces, converting motion energy into heat.\nSteps:\n1. Friction opposes sliding between surfaces, converting motion energy into heat.\n2. So the answer stands: Friction opposes sliding between surfaces, converting motion energy into heat."}
{"id": "phy_0218", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what is energy per charge?", "choices": {"A": "Voltage", "B": "Current", "C": "Power", "D": "Force"}, "answer": "The answer is Voltage.", "steps": ["Volts push flow.", "So: Voltage.", "Select option A."], "text": "Answer: Voltage\nSteps:\n1. Volts push flow.\n2. So: Voltage.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0219", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 5 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 41860 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 5 K.", "= 41860 J."], "text": "Answer: Heat: 41860 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 5 K.\n2. = 41860 J."}
{"id": "phy_0220", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 60 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 6×.", "steps": ["M = di/do.", "M = 60 cm / 10 cm.", "= 6×."], "text": "Answer: Magnification: 6×.\nSteps:\n1. M = di/do.\n2. M = 60 cm / 10 cm.\n3. = 6×."}
{"id": "phy_0221", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 6 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 2040 m.", "steps": ["d = v×t.", "d = 340 m/s × 6 s.", "= 2040 m."], "text": "Answer: Distance: 2040 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 6 s.\n3. = 2040 m."}
{"id": "phy_0222", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 7. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 21.", "steps": ["Pairs: 7×6/2.", "= 42/2.", "= 21."], "text": "Answer: Lines: 21.\nSteps:\n1. Pairs: 7×6/2.\n2. = 42/2.\n3. = 21."}
{"id": "phy_0223", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what is force times distance?", "choices": {"A": "Power", "B": "Work", "C": "Torque", "D": "Impulse"}, "answer": "The answer is Work.", "steps": ["Joules counted.", "So: Work.", "Select option B."], "text": "Answer: Work\nSteps:\n1. Joules counted.\n2. So: Work.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0224", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 6 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 108 W.", "steps": ["P = I²×R.", "P = (6 A)² × 3 Ω.", "= 108 W."], "text": "Answer: Power: 108 W.\nSteps:\n1. P = I²×R.\n2. P = (6 A)² × 3 Ω.\n3. = 108 W."}
{"id": "phy_0225", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what caps all engines?", "choices": {"A": "Speed limit", "B": "Carnot limit", "C": "Weight limit", "D": "Age limit"}, "answer": "The answer is Carnot limit.", "steps": ["Temps ratio bound.", "So: Carnot limit.", "Select option B."], "text": "Answer: Carnot limit\nSteps:\n1. Temps ratio bound.\n2. So: Carnot limit.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0226", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is dispersion?", "choices": null, "answer": "Glass bends colours differently, splitting white into rainbows.", "steps": ["Glass bends colours differently, splitting white into rainbows.", "So the answer stands: Glass bends colours differently, splitting white into rainbows."], "text": "Answer: Glass bends colours differently, splitting white into rainbows.\nSteps:\n1. Glass bends colours differently, splitting white into rainbows.\n2. So the answer stands: Glass bends colours differently, splitting white into rainbows."}
{"id": "phy_0227", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 120 Hz. What is its 3rd harmonic?", "choices": {"A": "330 Hz", "B": "390 Hz", "C": "420 Hz", "D": "360 Hz"}, "answer": "3rd harmonic is 360 Hz.", "steps": ["f3 = 3 × 120 Hz.", "f3 = 360 Hz.", "Select option D."], "text": "Answer: 360 Hz\nSteps:\n1. f3 = 3 × 120 Hz.\n2. f3 = 360 Hz.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0228", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Vzorek 400 atomů projde 2 poločasy. Kolik atomů zbude?", "choices": {"A": "100", "B": "50", "C": "150", "D": "200"}, "answer": "Zbude 100 atomů.", "steps": ["Půlit dvakrát: 400 → 200 → 100.", "Zbývá: 100.", "Vyber možnost A."], "text": "Answer: 100\nSteps:\n1. Půlit dvakrát: 400 → 200 → 100.\n2. Zbývá: 100.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0229", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why use free-body diagrams?", "choices": null, "answer": "They isolate one body with all force arrows, making Newton's laws easy to apply.", "steps": ["They isolate one body with all force arrows, making Newton's laws easy to apply.", "So the answer stands: They isolate one body with all force arrows, making Newton's laws easy to apply."], "text": "Answer: They isolate one body with all force arrows, making Newton's laws easy to apply.\nSteps:\n1. They isolate one body with all force arrows, making Newton's laws easy to apply.\n2. So the answer stands: They isolate one body with all force arrows, making Newton's laws easy to apply."}
{"id": "phy_0230", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Proud 4 A teče po 10 s. Kolik náboje projde?", "choices": {"A": "20 C", "B": "60 C", "C": "40 C", "D": "80 C"}, "answer": "Náboj je 40 C.", "steps": ["Q = 4 A × 10 s.", "Q = 40 C.", "Vyber možnost C."], "text": "Answer: 40 C\nSteps:\n1. Q = 4 A × 10 s.\n2. Q = 40 C.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0231", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Kolik tepla ohřeje 1 kg vody o 2 K? (c = 4186 J/(kg·K))", "choices": {"A": "4186 J", "B": "8372 J", "C": "12558 J", "D": "16744 J"}, "answer": "Teplo je 8372 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 2 K.", "Q = 8372 J.", "Vyber možnost B."], "text": "Answer: 8372 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 2 K.\n2. Q = 8372 J.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0232", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Obraz vzniká 40 cm od čočky, předmět v 10 cm. Spočítej zvětšení.", "choices": null, "answer": "Zvětšení: 4×.", "steps": ["M = di/do.", "M = 40 cm / 10 cm.", "= 4×."], "text": "Answer: Zvětšení: 4×.\nSteps:\n1. M = di/do.\n2. M = 40 cm / 10 cm.\n3. = 4×."}
{"id": "phy_0233", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co nese bez látky?", "choices": {"A": "vítr", "B": "řeka", "C": "nákladní auto", "D": "vlna"}, "answer": "Odpověď je vlna.", "steps": ["Energie cestuje.", "Tedy: vlna.", "Vyber možnost D."], "text": "Answer: vlna\nSteps:\n1. Energie cestuje.\n2. Tedy: vlna.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0234", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 3 protons and 3 neutrons. What is its mass number?", "choices": {"A": "5", "B": "7", "C": "8", "D": "6"}, "answer": "Mass number is 6.", "steps": ["A = 3 + 3.", "A = 6.", "Select option D."], "text": "Answer: 6\nSteps:\n1. A = 3 + 3.\n2. A = 6.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0235", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is weight?", "choices": null, "answer": "Weight is gravity's pull mg on mass, so it changes with planet while mass stays fixed.", "steps": ["Weight is gravity's pull mg on mass, so it changes with planet while mass stays fixed.", "So the answer stands: Weight is gravity's pull mg on mass, so it changes with planet while mass stays fixed."], "text": "Answer: Weight is gravity's pull mg on mass, so it changes with planet while mass stays fixed.\nSteps:\n1. Weight is gravity's pull mg on mass, so it changes with planet while mass stays fixed.\n2. So the answer stands: Weight is gravity's pull mg on mass, so it changes with planet while mass stays fixed."}
{"id": "phy_0236", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 6 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 72 V.", "steps": ["V = I×R.", "V = 6 A × 12 Ω.", "= 72 V."], "text": "Answer: Voltage: 72 V.\nSteps:\n1. V = I×R.\n2. V = 6 A × 12 Ω.\n3. = 72 V."}
{"id": "phy_0237", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 22 °C. What is it in kelvin?", "choices": {"A": "294 K", "B": "296 K", "C": "295 K", "D": "297 K"}, "answer": "Temperature is 295 K.", "steps": ["22 °C + 273.", "= 295 K.", "Select option C."], "text": "Answer: 295 K\nSteps:\n1. 22 °C + 273.\n2. = 295 K.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0238", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 40 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "3×", "B": "5×", "C": "4×", "D": "6×"}, "answer": "Magnification is 4×.", "steps": ["M = 40 cm / 10 cm.", "M = 4×.", "Select option C."], "text": "Answer: 4×\nSteps:\n1. M = 40 cm / 10 cm.\n2. M = 4×.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0239", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what links speed, cycles?", "choices": {"A": "v equals fλ", "B": "E equals mc", "C": "F equals ma", "D": "pV equals nRT"}, "answer": "The answer is v equals fλ.", "steps": ["Master relation held.", "So: v equals fλ.", "Select option A."], "text": "Answer: v equals fλ\nSteps:\n1. Master relation held.\n2. So: v equals fλ.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0240", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is quantum mechanics?", "choices": null, "answer": "Tiny scales follow wave rules with discrete outcomes and uncertainty.", "steps": ["Tiny scales follow wave rules with discrete outcomes and uncertainty.", "So the answer stands: Tiny scales follow wave rules with discrete outcomes and uncertainty."], "text": "Answer: Tiny scales follow wave rules with discrete outcomes and uncertainty.\nSteps:\n1. Tiny scales follow wave rules with discrete outcomes and uncertainty.\n2. So the answer stands: Tiny scales follow wave rules with discrete outcomes and uncertainty."}
{"id": "phy_0241", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 4 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "9 N", "B": "15 N", "C": "12 N", "D": "18 N"}, "answer": "Net force is 12 N.", "steps": ["F = 4 kg × 3 m/s².", "F = 12 N.", "Select option C."], "text": "Answer: 12 N\nSteps:\n1. F = 4 kg × 3 m/s².\n2. F = 12 N.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0242", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 10 s. Compute the energy used.", "choices": null, "answer": "Energy: 1000 J.", "steps": ["E = P×t.", "E = 100 W × 10 s.", "= 1000 J."], "text": "Answer: Energy: 1000 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 10 s.\n3. = 1000 J."}
{"id": "phy_0243", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Motor mění 200 J z 1000 J tepla v práci. Jaká je jeho účinnost?", "choices": {"A": "10 %", "B": "30 %", "C": "20 %", "D": "40 %"}, "answer": "Účinnost je 20 %.", "steps": ["200 J / 1000 J.", "= 20 %.", "Vyber možnost C."], "text": "Answer: 20 %\nSteps:\n1. 200 J / 1000 J.\n2. = 20 %.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0244", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 13×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 4.3 s.", "steps": ["t = d/c.", "t = 13×10⁸ / 3×10⁸ s.", "= 4.3 s."], "text": "Answer: Time: 4.3 s.\nSteps:\n1. t = d/c.\n2. t = 13×10⁸ / 3×10⁸ s.\n3. = 4.3 s."}
{"id": "phy_0245", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co barví témbr?", "choices": {"A": "harmonické", "B": "statiky", "C": "hluky", "D": "ticha"}, "answer": "Odpověď je harmonické.", "steps": ["Svrchní přidány.", "Tedy: harmonické.", "Vyber možnost A."], "text": "Answer: harmonické\nSteps:\n1. Svrchní přidány.\n2. Tedy: harmonické.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0246", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what ticks slower?", "choices": {"A": "Moving clocks", "B": "Broken watches", "C": "Stopped timers", "D": "Lost phones"}, "answer": "The answer is Moving clocks.", "steps": ["Muons confirm.", "So: Moving clocks.", "Select option A."], "text": "Answer: Moving clocks\nSteps:\n1. Muons confirm.\n2. So: Moving clocks.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0247", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 7 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 14 N.", "steps": ["F = m×a.", "F = 7 kg × 2 m/s².", "= 14 N."], "text": "Answer: Net force: 14 N.\nSteps:\n1. F = m×a.\n2. F = 7 kg × 2 m/s².\n3. = 14 N."}
{"id": "phy_0248", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Proč Coulombův zákon?", "choices": null, "answer": "Síla škáluje s náboji a druhou mocninou vzdálenosti.", "steps": ["Síla škáluje s náboji a druhou mocninou vzdálenosti.", "Odpověď tedy platí: Síla škáluje s náboji a druhou mocninou vzdálenosti."], "text": "Answer: Síla škáluje s náboji a druhou mocninou vzdálenosti.\nSteps:\n1. Síla škáluje s náboji a druhou mocninou vzdálenosti.\n2. Odpověď tedy platí: Síla škáluje s náboji a druhou mocninou vzdálenosti."}
{"id": "phy_0249", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 4 K? (c = 4186 J/(kg·K))", "choices": {"A": "12558 J", "B": "20930 J", "C": "25116 J", "D": "16744 J"}, "answer": "Heat needed is 16744 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 4 K.", "Q = 16744 J.", "Select option D."], "text": "Answer: 16744 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 4 K.\n2. Q = 16744 J.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0250", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why rainbows?", "choices": null, "answer": "Drops refract, reflect, and disperse sunlight at 42 degrees to watchers.", "steps": ["Drops refract, reflect, and disperse sunlight at 42 degrees to watchers.", "So the answer stands: Drops refract, reflect, and disperse sunlight at 42 degrees to watchers."], "text": "Answer: Drops refract, reflect, and disperse sunlight at 42 degrees to watchers.\nSteps:\n1. Drops refract, reflect, and disperse sunlight at 42 degrees to watchers.\n2. So the answer stands: Drops refract, reflect, and disperse sunlight at 42 degrees to watchers."}
{"id": "phy_0251", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 140 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 420 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 140 Hz.", "= 420 Hz."], "text": "Answer: 3rd harmonic: 420 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 140 Hz.\n3. = 420 Hz."}
{"id": "phy_0252", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what merges light?", "choices": {"A": "Confusion", "B": "Fusion", "C": "Diffusion", "D": "Illusion"}, "answer": "The answer is Fusion.", "steps": ["Stars lit.", "So: Fusion.", "Select option B."], "text": "Answer: Fusion\nSteps:\n1. Stars lit.\n2. So: Fusion.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0253", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 4 kg zrychluje 2 m/s². Spočítej výslednou sílu.", "choices": null, "answer": "Výsledná síla: 8 N.", "steps": ["F = m×a.", "F = 4 kg × 2 m/s².", "= 8 N."], "text": "Answer: Výsledná síla: 8 N.\nSteps:\n1. F = m×a.\n2. F = 4 kg × 2 m/s².\n3. = 8 N."}
{"id": "phy_0254", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why series adds?", "choices": null, "answer": "Series resistors share one current, so voltages stack across each in turn.", "steps": ["Series resistors share one current, so voltages stack across each in turn.", "So the answer stands: Series resistors share one current, so voltages stack across each in turn."], "text": "Answer: Series resistors share one current, so voltages stack across each in turn.\nSteps:\n1. Series resistors share one current, so voltages stack across each in turn.\n2. So the answer stands: Series resistors share one current, so voltages stack across each in turn."}
{"id": "phy_0255", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is the second law?", "choices": null, "answer": "Entropy of isolated systems never falls, forcing heat toward uniform spread.", "steps": ["Entropy of isolated systems never falls, forcing heat toward uniform spread.", "So the answer stands: Entropy of isolated systems never falls, forcing heat toward uniform spread."], "text": "Answer: Entropy of isolated systems never falls, forcing heat toward uniform spread.\nSteps:\n1. Entropy of isolated systems never falls, forcing heat toward uniform spread.\n2. So the answer stands: Entropy of isolated systems never falls, forcing heat toward uniform spread."}
{"id": "phy_0256", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is diffraction?", "choices": null, "answer": "Waves bend around edges and slits, proving light's wave nature.", "steps": ["Waves bend around edges and slits, proving light's wave nature.", "So the answer stands: Waves bend around edges and slits, proving light's wave nature."], "text": "Answer: Waves bend around edges and slits, proving light's wave nature.\nSteps:\n1. Waves bend around edges and slits, proving light's wave nature.\n2. So the answer stands: Waves bend around edges and slits, proving light's wave nature."}
{"id": "phy_0257", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what logs loudness?", "choices": {"A": "Metre", "B": "Decibel", "C": "Second", "D": "Gram"}, "answer": "The answer is Decibel.", "steps": ["Power ratioed.", "So: Decibel.", "Select option B."], "text": "Answer: Decibel\nSteps:\n1. Power ratioed.\n2. So: Decibel.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0258", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 6 protons and 7 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 13.", "steps": ["A = Z+N.", "A = 6 + 7.", "= 13."], "text": "Answer: Mass number: 13.\nSteps:\n1. A = Z+N.\n2. A = 6 + 7.\n3. = 13."}
{"id": "phy_0259", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why g is 9.8?", "choices": null, "answer": "Earth's mass and radius set surface gravity near 9.8 m/s², weaker on the Moon.", "steps": ["Earth's mass and radius set surface gravity near 9.8 m/s², weaker on the Moon.", "So the answer stands: Earth's mass and radius set surface gravity near 9.8 m/s², weaker on the Moon."], "text": "Answer: Earth's mass and radius set surface gravity near 9.8 m/s², weaker on the Moon.\nSteps:\n1. Earth's mass and radius set surface gravity near 9.8 m/s², weaker on the Moon.\n2. So the answer stands: Earth's mass and radius set surface gravity near 9.8 m/s², weaker on the Moon."}
{"id": "phy_0260", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is parallel for?", "choices": null, "answer": "Parallel branches share voltage while splitting current, keeping bulbs bright.", "steps": ["Parallel branches share voltage while splitting current, keeping bulbs bright.", "So the answer stands: Parallel branches share voltage while splitting current, keeping bulbs bright."], "text": "Answer: Parallel branches share voltage while splitting current, keeping bulbs bright.\nSteps:\n1. Parallel branches share voltage while splitting current, keeping bulbs bright.\n2. So the answer stands: Parallel branches share voltage while splitting current, keeping bulbs bright."}
{"id": "phy_0261", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 900 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 90 W.", "steps": ["P = W/t.", "P = 900 J / 10 s.", "= 90 W."], "text": "Answer: Power: 90 W.\nSteps:\n1. P = W/t.\n2. P = 900 J / 10 s.\n3. = 90 W."}
{"id": "phy_0262", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 9×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "4 s", "B": "5 s", "C": "2 s", "D": "3 s"}, "answer": "Time is 3 s.", "steps": ["t = 9×10⁸ m / 3×10⁸ m/s.", "t = 3 s.", "Select option D."], "text": "Answer: 3 s\nSteps:\n1. t = 9×10⁸ m / 3×10⁸ m/s.\n2. t = 3 s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0263", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 200 Hz and λ = 2 m. What is its speed?", "choices": {"A": "350 m/s", "B": "450 m/s", "C": "400 m/s", "D": "500 m/s"}, "answer": "Speed is 400 m/s.", "steps": ["v = 200 Hz × 2 m.", "v = 400 m/s.", "Select option C."], "text": "Answer: 400 m/s\nSteps:\n1. v = 200 Hz × 2 m.\n2. v = 400 m/s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0264", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 4000 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 1000.", "steps": ["Halve: 4000 → 2000.", "Halve: 2000 → 1000.", "= 1000."], "text": "Answer: Survivors: 1000.\nSteps:\n1. Halve: 4000 → 2000.\n2. Halve: 2000 → 1000.\n3. = 1000."}
{"id": "phy_0265", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Síla 15 N tlačí na dráze 4 m. Spočítej vykonanou práci.", "choices": null, "answer": "Práce: 60 J.", "steps": ["W = F×d.", "W = 15 N × 4 m.", "= 60 J."], "text": "Answer: Práce: 60 J.\nSteps:\n1. W = F×d.\n2. W = 15 N × 4 m.\n3. = 60 J."}
{"id": "phy_0266", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why Kirchhoff's rules?", "choices": null, "answer": "Charge and energy conservation force currents to balance and loops to sum zero.", "steps": ["Charge and energy conservation force currents to balance and loops to sum zero.", "So the answer stands: Charge and energy conservation force currents to balance and loops to sum zero."], "text": "Answer: Charge and energy conservation force currents to balance and loops to sum zero.\nSteps:\n1. Charge and energy conservation force currents to balance and loops to sum zero.\n2. So the answer stands: Charge and energy conservation force currents to balance and loops to sum zero."}
{"id": "phy_0267", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 20 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 293 K.", "steps": ["Add 273.", "20 + 273.", "= 293 K."], "text": "Answer: Temperature: 293 K.\nSteps:\n1. Add 273.\n2. 20 + 273.\n3. = 293 K."}
{"id": "phy_0268", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why interference?", "choices": null, "answer": "Overlapping waves add or cancel by phase, painting fringes and colours.", "steps": ["Overlapping waves add or cancel by phase, painting fringes and colours.", "So the answer stands: Overlapping waves add or cancel by phase, painting fringes and colours."], "text": "Answer: Overlapping waves add or cancel by phase, painting fringes and colours.\nSteps:\n1. Overlapping waves add or cancel by phase, painting fringes and colours.\n2. So the answer stands: Overlapping waves add or cancel by phase, painting fringes and colours."}
{"id": "phy_0269", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 450 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1350 m/s.", "steps": ["v = f×λ.", "v = 450 Hz × 3 m.", "= 1350 m/s."], "text": "Answer: Speed: 1350 m/s.\nSteps:\n1. v = f×λ.\n2. v = 450 Hz × 3 m.\n3. = 1350 m/s."}
{"id": "phy_0270", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why quantization?", "choices": null, "answer": "Bound systems allow only ladder energies, painting spectral lines.", "steps": ["Bound systems allow only ladder energies, painting spectral lines.", "So the answer stands: Bound systems allow only ladder energies, painting spectral lines."], "text": "Answer: Bound systems allow only ladder energies, painting spectral lines.\nSteps:\n1. Bound systems allow only ladder energies, painting spectral lines.\n2. So the answer stands: Bound systems allow only ladder energies, painting spectral lines."}
{"id": "phy_0271", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Co je tíha?", "choices": null, "answer": "Tíha je gravitační tah mg na hmotnost.", "steps": ["Tíha je gravitační tah mg na hmotnost.", "Odpověď tedy platí: Tíha je gravitační tah mg na hmotnost."], "text": "Answer: Tíha je gravitační tah mg na hmotnost.\nSteps:\n1. Tíha je gravitační tah mg na hmotnost.\n2. Odpověď tedy platí: Tíha je gravitační tah mg na hmotnost."}
{"id": "phy_0272", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Co je elektrické pole?", "choices": null, "answer": "Pole mapuje sílu na náboj prostorem.", "steps": ["Pole mapuje sílu na náboj prostorem.", "Odpověď tedy platí: Pole mapuje sílu na náboj prostorem."], "text": "Answer: Pole mapuje sílu na náboj prostorem.\nSteps:\n1. Pole mapuje sílu na náboj prostorem.\n2. Odpověď tedy platí: Pole mapuje sílu na náboj prostorem."}
{"id": "phy_0273", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 400 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "40%", "B": "30%", "C": "50%", "D": "60%"}, "answer": "Efficiency is 40%.", "steps": ["400 J / 1000 J.", "= 40%.", "Select option A."], "text": "Answer: 40%\nSteps:\n1. 400 J / 1000 J.\n2. = 40%.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0274", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 60 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "40 cm", "B": "35 cm", "C": "45 cm", "D": "50 cm"}, "answer": "Apparent depth is 40 cm.", "steps": ["d' = 60 cm / 1.5.", "d' = 40 cm.", "Select option A."], "text": "Answer: 40 cm\nSteps:\n1. d' = 60 cm / 1.5.\n2. d' = 40 cm.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0275", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 7 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 2380 m.", "steps": ["d = v×t.", "d = 340 m/s × 7 s.", "= 2380 m."], "text": "Answer: Distance: 2380 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 7 s.\n3. = 2380 m."}
{"id": "phy_0276", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 8. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 28.", "steps": ["Pairs: 8×7/2.", "= 56/2.", "= 28."], "text": "Answer: Lines: 28.\nSteps:\n1. Pairs: 8×7/2.\n2. = 56/2.\n3. = 28."}
{"id": "phy_0277", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 6 kg se pohybuje 3 m/s. Spočítej jeho hybnost.", "choices": null, "answer": "Hybnost: 18 kg·m/s.", "steps": ["p = m×v.", "p = 6 kg × 3 m/s.", "= 18 kg·m/s."], "text": "Answer: Hybnost: 18 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 6 kg × 3 m/s.\n3. = 18 kg·m/s."}
{"id": "phy_0278", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 7 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 147 W.", "steps": ["P = I²×R.", "P = (7 A)² × 3 Ω.", "= 147 W."], "text": "Answer: Power: 147 W.\nSteps:\n1. P = I²×R.\n2. P = (7 A)² × 3 Ω.\n3. = 147 W."}
{"id": "phy_0279", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Teplota je 16 °C. Převeď ji na kelviny.", "choices": null, "answer": "Teplota: 289 K.", "steps": ["Přičti 273.", "16 + 273.", "= 289 K."], "text": "Answer: Teplota: 289 K.\nSteps:\n1. Přičti 273.\n2. 16 + 273.\n3. = 289 K."}
{"id": "phy_0280", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 90 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 60 cm.", "steps": ["d' = d/n.", "d' = 90 cm / 1.5.", "= 60 cm."], "text": "Answer: Apparent depth: 60 cm.\nSteps:\n1. d' = d/n.\n2. d' = 90 cm / 1.5.\n3. = 60 cm."}
{"id": "phy_0281", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 150 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 450 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 150 Hz.", "= 450 Hz."], "text": "Answer: 3rd harmonic: 450 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 150 Hz.\n3. = 450 Hz."}
{"id": "phy_0282", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Co je kontrakce délek?", "choices": null, "answer": "Rychlé předměty se krátí ve směru pohybu.", "steps": ["Rychlé předměty se krátí ve směru pohybu.", "Odpověď tedy platí: Rychlé předměty se krátí ve směru pohybu."], "text": "Answer: Rychlé předměty se krátí ve směru pohybu.\nSteps:\n1. Rychlé předměty se krátí ve směru pohybu.\n2. Odpověď tedy platí: Rychlé předměty se krátí ve směru pohybu."}
{"id": "phy_0283", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 30 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 120 J.", "steps": ["W = F×d.", "W = 30 N × 4 m.", "= 120 J."], "text": "Answer: Work: 120 J.\nSteps:\n1. W = F×d.\n2. W = 30 N × 4 m.\n3. = 120 J."}
{"id": "phy_0284", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is capacitance?", "choices": null, "answer": "Capacitors store charge per volt, smoothing supplies and timing circuits.", "steps": ["Capacitors store charge per volt, smoothing supplies and timing circuits.", "So the answer stands: Capacitors store charge per volt, smoothing supplies and timing circuits."], "text": "Answer: Capacitors store charge per volt, smoothing supplies and timing circuits.\nSteps:\n1. Capacitors store charge per volt, smoothing supplies and timing circuits.\n2. So the answer stands: Capacitors store charge per volt, smoothing supplies and timing circuits."}
{"id": "phy_0285", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 6 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 50232 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 6 K.", "= 50232 J."], "text": "Answer: Heat: 50232 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 6 K.\n2. = 50232 J."}
{"id": "phy_0286", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Předmět leží 30 cm hluboko ve skle (n = 1,5). Jaká je zdánlivá hloubka?", "choices": {"A": "15 cm", "B": "25 cm", "C": "20 cm", "D": "30 cm"}, "answer": "Zdánlivá hloubka je 20 cm.", "steps": ["d' = 30 cm / 1,5.", "d' = 20 cm.", "Vyber možnost C."], "text": "Answer: 20 cm\nSteps:\n1. d' = 30 cm / 1,5.\n2. d' = 20 cm.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0287", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 4 Hz. What is its period?", "choices": {"A": "0.2 s", "B": "0.17 s", "C": "0.33 s", "D": "0.25 s"}, "answer": "Period is 0.25 s.", "steps": ["T = 1 / 4 Hz.", "T = 0.25 s.", "Select option D."], "text": "Answer: 0.25 s\nSteps:\n1. T = 1 / 4 Hz.\n2. T = 0.25 s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0288", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 1200 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "250", "B": "350", "C": "300", "D": "400"}, "answer": "300 atoms remain.", "steps": ["Halve twice: 1200 → 600 → 300.", "Left: 300.", "Select option C."], "text": "Answer: 300\nSteps:\n1. Halve twice: 1200 → 600 → 300.\n2. Left: 300.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0289", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 120 m in 10 s. What is its speed?", "choices": {"A": "11 m/s", "B": "13 m/s", "C": "14 m/s", "D": "12 m/s"}, "answer": "Speed is 12 m/s.", "steps": ["v = 120 m / 10 s.", "v = 12 m/s.", "Select option D."], "text": "Answer: 12 m/s\nSteps:\n1. v = 120 m / 10 s.\n2. v = 12 m/s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0290", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why RC time?", "choices": null, "answer": "Resistance times capacitance sets charge speed, timing flashes and filters.", "steps": ["Resistance times capacitance sets charge speed, timing flashes and filters.", "So the answer stands: Resistance times capacitance sets charge speed, timing flashes and filters."], "text": "Answer: Resistance times capacitance sets charge speed, timing flashes and filters.\nSteps:\n1. Resistance times capacitance sets charge speed, timing flashes and filters.\n2. So the answer stands: Resistance times capacitance sets charge speed, timing flashes and filters."}
{"id": "phy_0291", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1000 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 100 W.", "steps": ["P = W/t.", "P = 1000 J / 10 s.", "= 100 W."], "text": "Answer: Power: 100 W.\nSteps:\n1. P = W/t.\n2. P = 1000 J / 10 s.\n3. = 100 W."}
{"id": "phy_0292", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 70 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 7×.", "steps": ["M = di/do.", "M = 70 cm / 10 cm.", "= 7×."], "text": "Answer: Magnification: 7×.\nSteps:\n1. M = di/do.\n2. M = 70 cm / 10 cm.\n3. = 7×."}
{"id": "phy_0293", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 500 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1500 m/s.", "steps": ["v = f×λ.", "v = 500 Hz × 3 m.", "= 1500 m/s."], "text": "Answer: Speed: 1500 m/s.\nSteps:\n1. v = f×λ.\n2. v = 500 Hz × 3 m.\n3. = 1500 m/s."}
{"id": "phy_0294", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 5. How many spectral lines can it emit?", "choices": {"A": "9", "B": "11", "C": "12", "D": "10"}, "answer": "Count: 10.", "steps": ["Pairs: 5×4/2.", "Lines: 10.", "Select option D."], "text": "Answer: 10\nSteps:\n1. Pairs: 5×4/2.\n2. Lines: 10.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0295", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 5 kg zrychluje 2 m/s². Spočítej výslednou sílu.", "choices": null, "answer": "Výsledná síla: 10 N.", "steps": ["F = m×a.", "F = 5 kg × 2 m/s².", "= 10 N."], "text": "Answer: Výsledná síla: 10 N.\nSteps:\n1. F = m×a.\n2. F = 5 kg × 2 m/s².\n3. = 10 N."}
{"id": "phy_0296", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is magnetism?", "choices": null, "answer": "Moving charges create magnetic fields, turning compasses and motors alike.", "steps": ["Moving charges create magnetic fields, turning compasses and motors alike.", "So the answer stands: Moving charges create magnetic fields, turning compasses and motors alike."], "text": "Answer: Moving charges create magnetic fields, turning compasses and motors alike.\nSteps:\n1. Moving charges create magnetic fields, turning compasses and motors alike.\n2. So the answer stands: Moving charges create magnetic fields, turning compasses and motors alike."}
{"id": "phy_0297", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 21 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 294 K.", "steps": ["Add 273.", "21 + 273.", "= 294 K."], "text": "Answer: Temperature: 294 K.\nSteps:\n1. Add 273.\n2. 21 + 273.\n3. = 294 K."}
{"id": "phy_0298", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co se odráží stejně?", "choices": {"A": "lom", "B": "rozptyl", "C": "pohlcení", "D": "odraz"}, "answer": "Odpověď je odraz.", "steps": ["Úhly shodné.", "Tedy: odraz.", "Vyber možnost D."], "text": "Answer: odraz\nSteps:\n1. Úhly shodné.\n2. Tedy: odraz.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0299", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is a transverse wave?", "choices": null, "answer": "Shakes run perpendicular to travel, like light and strings.", "steps": ["Shakes run perpendicular to travel, like light and strings.", "So the answer stands: Shakes run perpendicular to travel, like light and strings."], "text": "Answer: Shakes run perpendicular to travel, like light and strings.\nSteps:\n1. Shakes run perpendicular to travel, like light and strings.\n2. So the answer stands: Shakes run perpendicular to travel, like light and strings."}
{"id": "phy_0300", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Atom je vybuzen do hladiny n = 3. Kolik spektrálních čar může vyzářit?", "choices": {"A": "2", "B": "3", "C": "4", "D": "5"}, "answer": "Počet: 3.", "steps": ["Dvojice: 3×2/2.", "Čar: 3.", "Vyber možnost B."], "text": "Answer: 3\nSteps:\n1. Dvojice: 3×2/2.\n2. Čar: 3.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0301", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Síla 20 N tlačí na dráze 4 m. Spočítej vykonanou práci.", "choices": null, "answer": "Práce: 80 J.", "steps": ["W = F×d.", "W = 20 N × 4 m.", "= 80 J."], "text": "Answer: Práce: 80 J.\nSteps:\n1. W = F×d.\n2. W = 20 N × 4 m.\n3. = 80 J."}
{"id": "phy_0302", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what scales by turns?", "choices": {"A": "Motor", "B": "Transformer", "C": "Battery", "D": "Fuse"}, "answer": "The answer is Transformer.", "steps": ["Voltage ratioed.", "So: Transformer.", "Select option B."], "text": "Answer: Transformer\nSteps:\n1. Voltage ratioed.\n2. So: Transformer.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0303", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Co je teplota?", "choices": null, "answer": "Teplota měří průměrnou kinetickou energii částic.", "steps": ["Teplota měří průměrnou kinetickou energii částic.", "Odpověď tedy platí: Teplota měří průměrnou kinetickou energii částic."], "text": "Answer: Teplota měří průměrnou kinetickou energii částic.\nSteps:\n1. Teplota měří průměrnou kinetickou energii částic.\n2. Odpověď tedy platí: Teplota měří průměrnou kinetickou energii částic."}
{"id": "phy_0304", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what predicts bends?", "choices": {"A": "Ohm's law", "B": "Snell's law", "C": "Hooke's law", "D": "Boyle's law"}, "answer": "The answer is Snell's law.", "steps": ["Sines scaled.", "So: Snell's law.", "Select option B."], "text": "Answer: Snell's law\nSteps:\n1. Sines scaled.\n2. So: Snell's law.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0305", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why longitudinal?", "choices": null, "answer": "Shakes run along travel in compressions, like sound in air.", "steps": ["Shakes run along travel in compressions, like sound in air.", "So the answer stands: Shakes run along travel in compressions, like sound in air."], "text": "Answer: Shakes run along travel in compressions, like sound in air.\nSteps:\n1. Shakes run along travel in compressions, like sound in air.\n2. So the answer stands: Shakes run along travel in compressions, like sound in air."}
{"id": "phy_0306", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is superposition?", "choices": null, "answer": "Quantum states blend possibilities until measurement picks one.", "steps": ["Quantum states blend possibilities until measurement picks one.", "So the answer stands: Quantum states blend possibilities until measurement picks one."], "text": "Answer: Quantum states blend possibilities until measurement picks one.\nSteps:\n1. Quantum states blend possibilities until measurement picks one.\n2. So the answer stands: Quantum states blend possibilities until measurement picks one."}
{"id": "phy_0307", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is projectile motion?", "choices": null, "answer": "Horizontal velocity stays constant while gravity accelerates downward, tracing a parabola.", "steps": ["Horizontal velocity stays constant while gravity accelerates downward, tracing a parabola.", "So the answer stands: Horizontal velocity stays constant while gravity accelerates downward, tracing a parabola."], "text": "Answer: Horizontal velocity stays constant while gravity accelerates downward, tracing a parabola.\nSteps:\n1. Horizontal velocity stays constant while gravity accelerates downward, tracing a parabola.\n2. So the answer stands: Horizontal velocity stays constant while gravity accelerates downward, tracing a parabola."}
{"id": "phy_0308", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why Lorentz force?", "choices": null, "answer": "Charges in fields feel qvB pushes sideways, bending beams and currents.", "steps": ["Charges in fields feel qvB pushes sideways, bending beams and currents.", "So the answer stands: Charges in fields feel qvB pushes sideways, bending beams and currents."], "text": "Answer: Charges in fields feel qvB pushes sideways, bending beams and currents.\nSteps:\n1. Charges in fields feel qvB pushes sideways, bending beams and currents.\n2. So the answer stands: Charges in fields feel qvB pushes sideways, bending beams and currents."}
{"id": "phy_0309", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Proč Kelvinova stupnice?", "choices": null, "answer": "Kelvin začíná v absolutní nule.", "steps": ["Kelvin začíná v absolutní nule.", "Odpověď tedy platí: Kelvin začíná v absolutní nule."], "text": "Answer: Kelvin začíná v absolutní nule.\nSteps:\n1. Kelvin začíná v absolutní nule.\n2. Odpověď tedy platí: Kelvin začíná v absolutní nule."}
{"id": "phy_0310", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what cuts glare?", "choices": {"A": "Amplifier", "B": "Heater", "C": "Polarizer", "D": "Timer"}, "answer": "The answer is Polarizer.", "steps": ["Direction filtered.", "So: Polarizer.", "Select option C."], "text": "Answer: Polarizer\nSteps:\n1. Direction filtered.\n2. So: Polarizer.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0311", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Co je frekvence?", "choices": null, "answer": "Počet cyklů za sekundu v hertzích.", "steps": ["Počet cyklů za sekundu v hertzích.", "Odpověď tedy platí: Počet cyklů za sekundu v hertzích."], "text": "Answer: Počet cyklů za sekundu v hertzích.\nSteps:\n1. Počet cyklů za sekundu v hertzích.\n2. Odpověď tedy platí: Počet cyklů za sekundu v hertzích."}
{"id": "phy_0312", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 4 protons and 4 neutrons. What is its mass number?", "choices": {"A": "8", "B": "7", "C": "9", "D": "10"}, "answer": "Mass number is 8.", "steps": ["A = 4 + 4.", "A = 8.", "Select option A."], "text": "Answer: 8\nSteps:\n1. A = 4 + 4.\n2. A = 8.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0313", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why independent axes?", "choices": null, "answer": "Perpendicular motions never affect each other, so x and y solve separately.", "steps": ["Perpendicular motions never affect each other, so x and y solve separately.", "So the answer stands: Perpendicular motions never affect each other, so x and y solve separately."], "text": "Answer: Perpendicular motions never affect each other, so x and y solve separately.\nSteps:\n1. Perpendicular motions never affect each other, so x and y solve separately.\n2. So the answer stands: Perpendicular motions never affect each other, so x and y solve separately."}
{"id": "phy_0314", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 7 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 84 V.", "steps": ["V = I×R.", "V = 7 A × 12 Ω.", "= 84 V."], "text": "Answer: Voltage: 84 V.\nSteps:\n1. V = I×R.\n2. V = 7 A × 12 Ω.\n3. = 84 V."}
{"id": "phy_0315", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co měří kmitání?", "choices": {"A": "tlak", "B": "objem", "C": "hmotnost", "D": "teplota"}, "answer": "Odpověď je teplota.", "steps": ["Průměrná energie čtena.", "Tedy: teplota.", "Vyber možnost D."], "text": "Answer: teplota\nSteps:\n1. Průměrná energie čtena.\n2. Tedy: teplota.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0316", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Co je Snellův zákon?", "choices": null, "answer": "n₁sinθ₁ rovná se n₂sinθ₂.", "steps": ["n₁sinθ₁ rovná se n₂sinθ₂.", "Odpověď tedy platí: n₁sinθ₁ rovná se n₂sinθ₂."], "text": "Answer: n₁sinθ₁ rovná se n₂sinθ₂.\nSteps:\n1. n₁sinθ₁ rovná se n₂sinθ₂.\n2. Odpověď tedy platí: n₁sinθ₁ rovná se n₂sinθ₂."}
{"id": "phy_0317", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 130 Hz. What is its 3rd harmonic?", "choices": {"A": "390 Hz", "B": "360 Hz", "C": "420 Hz", "D": "450 Hz"}, "answer": "3rd harmonic is 390 Hz.", "steps": ["f3 = 3 × 130 Hz.", "f3 = 390 Hz.", "Select option A."], "text": "Answer: 390 Hz\nSteps:\n1. f3 = 3 × 130 Hz.\n2. f3 = 390 Hz.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0318", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why entanglement?", "choices": null, "answer": "Linked particles correlate instantly across distance, violating local realism.", "steps": ["Linked particles correlate instantly across distance, violating local realism.", "So the answer stands: Linked particles correlate instantly across distance, violating local realism."], "text": "Answer: Linked particles correlate instantly across distance, violating local realism.\nSteps:\n1. Linked particles correlate instantly across distance, violating local realism.\n2. So the answer stands: Linked particles correlate instantly across distance, violating local realism."}
{"id": "phy_0319", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 6 m/s. What is its kinetic energy?", "choices": {"A": "36 J", "B": "30 J", "C": "42 J", "D": "48 J"}, "answer": "Kinetic energy is 36 J.", "steps": ["KE = ½×2 kg×(6 m/s)².", "KE = 36 J.", "Select option A."], "text": "Answer: 36 J\nSteps:\n1. KE = ½×2 kg×(6 m/s)².\n2. KE = 36 J.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0320", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 2 A teče přes 3 Ω. Spočítej ztrátový výkon.", "choices": null, "answer": "Výkon: 12 W.", "steps": ["P = I²×R.", "P = (2 A)² × 3 Ω.", "= 12 W."], "text": "Answer: Výkon: 12 W.\nSteps:\n1. P = I²×R.\n2. P = (2 A)² × 3 Ω.\n3. = 12 W."}
{"id": "phy_0321", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why heat engines?", "choices": null, "answer": "They turn heat flow into work between hot and cold, powering cars and plants.", "steps": ["They turn heat flow into work between hot and cold, powering cars and plants.", "So the answer stands: They turn heat flow into work between hot and cold, powering cars and plants."], "text": "Answer: They turn heat flow into work between hot and cold, powering cars and plants.\nSteps:\n1. They turn heat flow into work between hot and cold, powering cars and plants.\n2. So the answer stands: They turn heat flow into work between hot and cold, powering cars and plants."}
{"id": "phy_0322", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 50 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "4×", "B": "6×", "C": "7×", "D": "5×"}, "answer": "Magnification is 5×.", "steps": ["M = 50 cm / 10 cm.", "M = 5×.", "Select option D."], "text": "Answer: 5×\nSteps:\n1. M = 50 cm / 10 cm.\n2. M = 5×.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0323", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 8 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 2720 m.", "steps": ["d = v×t.", "d = 340 m/s × 8 s.", "= 2720 m."], "text": "Answer: Distance: 2720 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 8 s.\n3. = 2720 m."}
{"id": "phy_0324", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 7 protons and 8 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 15.", "steps": ["A = Z+N.", "A = 7 + 8.", "= 15."], "text": "Answer: Mass number: 15.\nSteps:\n1. A = Z+N.\n2. A = 7 + 8.\n3. = 15."}
{"id": "phy_0325", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is uniform circular motion?", "choices": null, "answer": "Speed stays fixed while direction turns, needing inward centripetal acceleration always.", "steps": ["Speed stays fixed while direction turns, needing inward centripetal acceleration always.", "So the answer stands: Speed stays fixed while direction turns, needing inward centripetal acceleration always."], "text": "Answer: Speed stays fixed while direction turns, needing inward centripetal acceleration always.\nSteps:\n1. Speed stays fixed while direction turns, needing inward centripetal acceleration always.\n2. So the answer stands: Speed stays fixed while direction turns, needing inward centripetal acceleration always."}
{"id": "phy_0326", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 11 s. Compute the energy used.", "choices": null, "answer": "Energy: 1100 J.", "steps": ["E = P×t.", "E = 100 W × 11 s.", "= 1100 J."], "text": "Answer: Energy: 1100 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 11 s.\n3. = 1100 J."}
{"id": "phy_0327", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 7 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 58604 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 7 K.", "= 58604 J."], "text": "Answer: Heat: 58604 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 7 K.\n2. = 58604 J."}
{"id": "phy_0328", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is Young's experiment?", "choices": null, "answer": "Double slits make fringe bands, measuring wavelengths precisely.", "steps": ["Double slits make fringe bands, measuring wavelengths precisely.", "So the answer stands: Double slits make fringe bands, measuring wavelengths precisely."], "text": "Answer: Double slits make fringe bands, measuring wavelengths precisely.\nSteps:\n1. Double slits make fringe bands, measuring wavelengths precisely.\n2. So the answer stands: Double slits make fringe bands, measuring wavelengths precisely."}
{"id": "phy_0329", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 160 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 480 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 160 Hz.", "= 480 Hz."], "text": "Answer: 3rd harmonic: 480 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 160 Hz.\n3. = 480 Hz."}
{"id": "phy_0330", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 4800 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 1200.", "steps": ["Halve: 4800 → 2400.", "Halve: 2400 → 1200.", "= 1200."], "text": "Answer: Survivors: 1200.\nSteps:\n1. Halve: 4800 → 2400.\n2. Halve: 2400 → 1200.\n3. = 1200."}
{"id": "phy_0331", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 9 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 27 kg·m/s.", "steps": ["p = m×v.", "p = 9 kg × 3 m/s.", "= 27 kg·m/s."], "text": "Answer: Momentum: 27 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 9 kg × 3 m/s.\n3. = 27 kg·m/s."}
{"id": "phy_0332", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is an electromagnet?", "choices": null, "answer": "Coiled current makes strong fields on demand, lifting scrap and ringing bells.", "steps": ["Coiled current makes strong fields on demand, lifting scrap and ringing bells.", "So the answer stands: Coiled current makes strong fields on demand, lifting scrap and ringing bells."], "text": "Answer: Coiled current makes strong fields on demand, lifting scrap and ringing bells.\nSteps:\n1. Coiled current makes strong fields on demand, lifting scrap and ringing bells.\n2. So the answer stands: Coiled current makes strong fields on demand, lifting scrap and ringing bells."}
{"id": "phy_0333", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is Carnot efficiency?", "choices": null, "answer": "It caps engines at 1 − Tc/Th, the best any heat cycle can do.", "steps": ["It caps engines at 1 − Tc/Th, the best any heat cycle can do.", "So the answer stands: It caps engines at 1 − Tc/Th, the best any heat cycle can do."], "text": "Answer: It caps engines at 1 − Tc/Th, the best any heat cycle can do.\nSteps:\n1. It caps engines at 1 − Tc/Th, the best any heat cycle can do.\n2. So the answer stands: It caps engines at 1 − Tc/Th, the best any heat cycle can do."}
{"id": "phy_0334", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 16×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 5.3 s.", "steps": ["t = d/c.", "t = 16×10⁸ / 3×10⁸ s.", "= 5.3 s."], "text": "Answer: Time: 5.3 s.\nSteps:\n1. t = d/c.\n2. t = 16×10⁸ / 3×10⁸ s.\n3. = 5.3 s."}
{"id": "phy_0335", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is sound?", "choices": null, "answer": "Air pressure waves from 20 Hz to 20 kHz that ears hear.", "steps": ["Air pressure waves from 20 Hz to 20 kHz that ears hear.", "So the answer stands: Air pressure waves from 20 Hz to 20 kHz that ears hear."], "text": "Answer: Air pressure waves from 20 Hz to 20 kHz that ears hear.\nSteps:\n1. Air pressure waves from 20 Hz to 20 kHz that ears hear.\n2. So the answer stands: Air pressure waves from 20 Hz to 20 kHz that ears hear."}
{"id": "phy_0336", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Jádro má 2 protonů a 2 neutronů. Jaké je jeho nukleonové číslo?", "choices": {"A": "3", "B": "5", "C": "4", "D": "6"}, "answer": "Nukleonové číslo je 4.", "steps": ["A = 2 + 2.", "A = 4.", "Vyber možnost C."], "text": "Answer: 4\nSteps:\n1. A = 2 + 2.\n2. A = 4.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0337", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 8 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 16 N.", "steps": ["F = m×a.", "F = 8 kg × 2 m/s².", "= 16 N."], "text": "Answer: Net force: 16 N.\nSteps:\n1. F = m×a.\n2. F = 8 kg × 2 m/s².\n3. = 16 N."}
{"id": "phy_0338", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why motors spin?", "choices": null, "answer": "Loop currents in fields feel twisting torques, converting electricity to motion.", "steps": ["Loop currents in fields feel twisting torques, converting electricity to motion.", "So the answer stands: Loop currents in fields feel twisting torques, converting electricity to motion."], "text": "Answer: Loop currents in fields feel twisting torques, converting electricity to motion.\nSteps:\n1. Loop currents in fields feel twisting torques, converting electricity to motion.\n2. So the answer stands: Loop currents in fields feel twisting torques, converting electricity to motion."}
{"id": "phy_0339", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Co je teplo?", "choices": null, "answer": "Teplo je energie proudící z tepla do chladu.", "steps": ["Teplo je energie proudící z tepla do chladu.", "Odpověď tedy platí: Teplo je energie proudící z tepla do chladu."], "text": "Answer: Teplo je energie proudící z tepla do chladu.\nSteps:\n1. Teplo je energie proudící z tepla do chladu.\n2. Odpověď tedy platí: Teplo je energie proudící z tepla do chladu."}
{"id": "phy_0340", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 12×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "4 s", "B": "5 s", "C": "6 s", "D": "3 s"}, "answer": "Time is 4 s.", "steps": ["t = 12×10⁸ m / 3×10⁸ m/s.", "t = 4 s.", "Select option A."], "text": "Answer: 4 s\nSteps:\n1. t = 12×10⁸ m / 3×10⁸ m/s.\n2. t = 4 s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0341", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Základ struny je 110 Hz. Spočítej její 3. harmonickou.", "choices": null, "answer": "3. harmonická: 330 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 110 Hz.", "= 330 Hz."], "text": "Answer: 3. harmonická: 330 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 110 Hz.\n3. = 330 Hz."}
{"id": "phy_0342", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 9. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 36.", "steps": ["Pairs: 9×8/2.", "= 72/2.", "= 36."], "text": "Answer: Lines: 36.\nSteps:\n1. Pairs: 9×8/2.\n2. = 72/2.\n3. = 36."}
{"id": "phy_0343", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 35 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 140 J.", "steps": ["W = F×d.", "W = 35 N × 4 m.", "= 140 J."], "text": "Answer: Work: 140 J.\nSteps:\n1. W = F×d.\n2. W = 35 N × 4 m.\n3. = 140 J."}
{"id": "phy_0344", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 2 A teče přes 12 Ω. Spočítej napětí.", "choices": null, "answer": "Napětí: 24 V.", "steps": ["U = I×R.", "U = 2 A × 12 Ω.", "= 24 V."], "text": "Answer: Napětí: 24 V.\nSteps:\n1. U = I×R.\n2. U = 2 A × 12 Ω.\n3. = 24 V."}
{"id": "phy_0345", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why refrigerators?", "choices": null, "answer": "They pump heat uphill with work input, cooling insides below room.", "steps": ["They pump heat uphill with work input, cooling insides below room.", "So the answer stands: They pump heat uphill with work input, cooling insides below room."], "text": "Answer: They pump heat uphill with work input, cooling insides below room.\nSteps:\n1. They pump heat uphill with work input, cooling insides below room.\n2. So the answer stands: They pump heat uphill with work input, cooling insides below room."}
{"id": "phy_0346", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why thin-film colours?", "choices": null, "answer": "Reflections from both film faces interfere, colouring bubbles and oil.", "steps": ["Reflections from both film faces interfere, colouring bubbles and oil.", "So the answer stands: Reflections from both film faces interfere, colouring bubbles and oil."], "text": "Answer: Reflections from both film faces interfere, colouring bubbles and oil.\nSteps:\n1. Reflections from both film faces interfere, colouring bubbles and oil.\n2. So the answer stands: Reflections from both film faces interfere, colouring bubbles and oil."}
{"id": "phy_0347", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what sets pitch?", "choices": {"A": "Amplitude", "B": "Frequency", "C": "Phase", "D": "Speed"}, "answer": "The answer is Frequency.", "steps": ["Hertz counted.", "So: Frequency.", "Select option B."], "text": "Answer: Frequency\nSteps:\n1. Hertz counted.\n2. So: Frequency.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0348", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 8 protons and 9 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 17.", "steps": ["A = Z+N.", "A = 8 + 9.", "= 17."], "text": "Answer: Mass number: 17.\nSteps:\n1. A = Z+N.\n2. A = 8 + 9.\n3. = 17."}
{"id": "phy_0349", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what pairs forces?", "choices": {"A": "Cause-delay", "B": "Action-reaction", "C": "Push-rest", "D": "Pull-sleep"}, "answer": "The answer is Action-reaction.", "steps": ["Third law pairs.", "So: Action-reaction.", "Select option B."], "text": "Answer: Action-reaction\nSteps:\n1. Third law pairs.\n2. So: Action-reaction.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0350", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co přitahuje opačné?", "choices": {"A": "hmotnost", "B": "spin", "C": "barva", "D": "náboj"}, "answer": "Odpověď je náboj.", "steps": ["Plus potkává minus.", "Tedy: náboj.", "Vyber možnost D."], "text": "Answer: náboj\nSteps:\n1. Plus potkává minus.\n2. Tedy: náboj.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0351", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1100 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 110 W.", "steps": ["P = W/t.", "P = 1100 J / 10 s.", "= 110 W."], "text": "Answer: Power: 110 W.\nSteps:\n1. P = W/t.\n2. P = 1100 J / 10 s.\n3. = 110 W."}
{"id": "phy_0352", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 75 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "45 cm", "B": "50 cm", "C": "55 cm", "D": "60 cm"}, "answer": "Apparent depth is 50 cm.", "steps": ["d' = 75 cm / 1.5.", "d' = 50 cm.", "Select option B."], "text": "Answer: 50 cm\nSteps:\n1. d' = 75 cm / 1.5.\n2. d' = 50 cm.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0353", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 550 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1650 m/s.", "steps": ["v = f×λ.", "v = 550 Hz × 3 m.", "= 1650 m/s."], "text": "Answer: Speed: 1650 m/s.\nSteps:\n1. v = f×λ.\n2. v = 550 Hz × 3 m.\n3. = 1650 m/s."}
{"id": "phy_0354", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is the double slit?", "choices": null, "answer": "Single particles build interference bands, proving self-wave nature.", "steps": ["Single particles build interference bands, proving self-wave nature.", "So the answer stands: Single particles build interference bands, proving self-wave nature."], "text": "Answer: Single particles build interference bands, proving self-wave nature.\nSteps:\n1. Single particles build interference bands, proving self-wave nature.\n2. So the answer stands: Single particles build interference bands, proving self-wave nature."}
{"id": "phy_0355", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why centripetal force?", "choices": null, "answer": "Inward net force bends paths into circles, from string tension to planetary gravity.", "steps": ["Inward net force bends paths into circles, from string tension to planetary gravity.", "So the answer stands: Inward net force bends paths into circles, from string tension to planetary gravity."], "text": "Answer: Inward net force bends paths into circles, from string tension to planetary gravity.\nSteps:\n1. Inward net force bends paths into circles, from string tension to planetary gravity.\n2. So the answer stands: Inward net force bends paths into circles, from string tension to planetary gravity."}
{"id": "phy_0356", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Co je napětí?", "choices": null, "answer": "Napětí je energie na náboj ve voltech.", "steps": ["Napětí je energie na náboj ve voltech.", "Odpověď tedy platí: Napětí je energie na náboj ve voltech."], "text": "Answer: Napětí je energie na náboj ve voltech.\nSteps:\n1. Napětí je energie na náboj ve voltech.\n2. Odpověď tedy platí: Napětí je energie na náboj ve voltech."}
{"id": "phy_0357", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what flows hot to cold?", "choices": {"A": "Work", "B": "Heat", "C": "Charge", "D": "Light"}, "answer": "The answer is Heat.", "steps": ["Joules moved.", "So: Heat.", "Select option B."], "text": "Answer: Heat\nSteps:\n1. Joules moved.\n2. So: Heat.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0358", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 105 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 70 cm.", "steps": ["d' = d/n.", "d' = 105 cm / 1.5.", "= 70 cm."], "text": "Answer: Apparent depth: 70 cm.\nSteps:\n1. d' = d/n.\n2. d' = 105 cm / 1.5.\n3. = 70 cm."}
{"id": "phy_0359", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why speed of sound?", "choices": null, "answer": "Air molecules pass hits at about 343 m/s, faster when warm.", "steps": ["Air molecules pass hits at about 343 m/s, faster when warm.", "So the answer stands: Air molecules pass hits at about 343 m/s, faster when warm."], "text": "Answer: Air molecules pass hits at about 343 m/s, faster when warm.\nSteps:\n1. Air molecules pass hits at about 343 m/s, faster when warm.\n2. So the answer stands: Air molecules pass hits at about 343 m/s, faster when warm."}
{"id": "phy_0360", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 5600 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 1400.", "steps": ["Halve: 5600 → 2800.", "Halve: 2800 → 1400.", "= 1400."], "text": "Answer: Survivors: 1400.\nSteps:\n1. Halve: 5600 → 2800.\n2. Halve: 2800 → 1400.\n3. = 1400."}
{"id": "phy_0361", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is work?", "choices": null, "answer": "Work is force times distance along motion, transferring energy measured in joules.", "steps": ["Work is force times distance along motion, transferring energy measured in joules.", "So the answer stands: Work is force times distance along motion, transferring energy measured in joules."], "text": "Answer: Work is force times distance along motion, transferring energy measured in joules.\nSteps:\n1. Work is force times distance along motion, transferring energy measured in joules.\n2. So the answer stands: Work is force times distance along motion, transferring energy measured in joules."}
{"id": "phy_0362", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows through 5 Ω. What is the voltage?", "choices": {"A": "15 V", "B": "25 V", "C": "20 V", "D": "30 V"}, "answer": "Voltage is 20 V.", "steps": ["V = 4 A × 5 Ω.", "V = 20 V.", "Select option C."], "text": "Answer: 20 V\nSteps:\n1. V = 4 A × 5 Ω.\n2. V = 20 V.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0363", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 22 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 295 K.", "steps": ["Add 273.", "22 + 273.", "= 295 K."], "text": "Answer: Temperature: 295 K.\nSteps:\n1. Add 273.\n2. 22 + 273.\n3. = 295 K."}
{"id": "phy_0364", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Světlo letí 7×10⁸ m. Spočítej dobu letu. (c = 3×10⁸ m/s)", "choices": null, "answer": "Čas: 2,3 s.", "steps": ["t = d/c.", "t = 7×10⁸ / 3×10⁸ s.", "= 2,3 s."], "text": "Answer: Čas: 2,3 s.\nSteps:\n1. t = d/c.\n2. t = 7×10⁸ / 3×10⁸ s.\n3. = 2,3 s."}
{"id": "phy_0365", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Proč v rovná se fλ?", "choices": null, "answer": "Rychlost rovná se cyklům krát délka.", "steps": ["Rychlost rovná se cyklům krát délka.", "Odpověď tedy platí: Rychlost rovná se cyklům krát délka."], "text": "Answer: Rychlost rovná se cyklům krát délka.\nSteps:\n1. Rychlost rovná se cyklům krát délka.\n2. Odpověď tedy platí: Rychlost rovná se cyklům krát délka."}
{"id": "phy_0366", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 10. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 45.", "steps": ["Pairs: 10×9/2.", "= 90/2.", "= 45."], "text": "Answer: Lines: 45.\nSteps:\n1. Pairs: 10×9/2.\n2. = 90/2.\n3. = 45."}
{"id": "phy_0367", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why kinetic energy?", "choices": null, "answer": "Moving mass carries ½mv² of energy, freed in braking or collisions.", "steps": ["Moving mass carries ½mv² of energy, freed in braking or collisions.", "So the answer stands: Moving mass carries ½mv² of energy, freed in braking or collisions."], "text": "Answer: Moving mass carries ½mv² of energy, freed in braking or collisions.\nSteps:\n1. Moving mass carries ½mv² of energy, freed in braking or collisions.\n2. So the answer stands: Moving mass carries ½mv² of energy, freed in braking or collisions."}
{"id": "phy_0368", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 8 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 192 W.", "steps": ["P = I²×R.", "P = (8 A)² × 3 Ω.", "= 192 W."], "text": "Answer: Power: 192 W.\nSteps:\n1. P = I²×R.\n2. P = (8 A)² × 3 Ω.\n3. = 192 W."}
{"id": "phy_0369", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Kolik tepla ohřeje 2 kg vody o 2 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Teplo: 16744 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 2 K.", "= 16744 J."], "text": "Answer: Teplo: 16744 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 2 K.\n2. = 16744 J."}
{"id": "phy_0370", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is polarization?", "choices": null, "answer": "Filtering oscillation direction cuts glare, used in sunglasses and screens.", "steps": ["Filtering oscillation direction cuts glare, used in sunglasses and screens.", "So the answer stands: Filtering oscillation direction cuts glare, used in sunglasses and screens."], "text": "Answer: Filtering oscillation direction cuts glare, used in sunglasses and screens.\nSteps:\n1. Filtering oscillation direction cuts glare, used in sunglasses and screens.\n2. So the answer stands: Filtering oscillation direction cuts glare, used in sunglasses and screens."}
{"id": "phy_0371", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 9 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 3060 m.", "steps": ["d = v×t.", "d = 340 m/s × 9 s.", "= 3060 m."], "text": "Answer: Distance: 3060 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 9 s.\n3. = 3060 m."}
{"id": "phy_0372", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 9 protons and 10 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 19.", "steps": ["A = Z+N.", "A = 9 + 10.", "= 19."], "text": "Answer: Mass number: 19.\nSteps:\n1. A = Z+N.\n2. A = 9 + 10.\n3. = 19."}
{"id": "phy_0373", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what persists in collisions?", "choices": {"A": "Speed", "B": "Heat", "C": "Momentum", "D": "Sound"}, "answer": "The answer is Momentum.", "steps": ["Sum conserved.", "So: Momentum.", "Select option C."], "text": "Answer: Momentum\nSteps:\n1. Sum conserved.\n2. So: Momentum.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0374", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is induction?", "choices": null, "answer": "Changing magnetic flux drives voltage in coils, the generator principle.", "steps": ["Changing magnetic flux drives voltage in coils, the generator principle.", "So the answer stands: Changing magnetic flux drives voltage in coils, the generator principle."], "text": "Answer: Changing magnetic flux drives voltage in coils, the generator principle.\nSteps:\n1. Changing magnetic flux drives voltage in coils, the generator principle.\n2. So the answer stands: Changing magnetic flux drives voltage in coils, the generator principle."}
{"id": "phy_0375", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Proč měrná kapacita?", "choices": null, "answer": "Je energie na hmotnost a stupeň, voda ji má vysokou.", "steps": ["Je energie na hmotnost a stupeň, voda ji má vysokou.", "Odpověď tedy platí: Je energie na hmotnost a stupeň, voda ji má vysokou."], "text": "Answer: Je energie na hmotnost a stupeň, voda ji má vysokou.\nSteps:\n1. Je energie na hmotnost a stupeň, voda ji má vysokou.\n2. Odpověď tedy platí: Je energie na hmotnost a stupeň, voda ji má vysokou."}
{"id": "phy_0376", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Proč úplný odraz?", "choices": null, "answer": "Za mezním úhlem se vše odráží uvnitř.", "steps": ["Za mezním úhlem se vše odráží uvnitř.", "Odpověď tedy platí: Za mezním úhlem se vše odráží uvnitř."], "text": "Answer: Za mezním úhlem se vše odráží uvnitř.\nSteps:\n1. Za mezním úhlem se vše odráží uvnitř.\n2. Odpověď tedy platí: Za mezním úhlem se vše odráží uvnitř."}
{"id": "phy_0377", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what images babies?", "choices": {"A": "X-ray", "B": "Gamma ray", "C": "Ultrasound", "D": "Microwave"}, "answer": "The answer is Ultrasound.", "steps": ["Echoes mapped.", "So: Ultrasound.", "Select option C."], "text": "Answer: Ultrasound\nSteps:\n1. Echoes mapped.\n2. So: Ultrasound.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0378", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 6400 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 1600.", "steps": ["Halve: 6400 → 3200.", "Halve: 3200 → 1600.", "= 1600."], "text": "Answer: Survivors: 1600.\nSteps:\n1. Halve: 6400 → 3200.\n2. Halve: 3200 → 1600.\n3. = 1600."}
{"id": "phy_0379", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 5 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "12 N", "B": "18 N", "C": "21 N", "D": "15 N"}, "answer": "Net force is 15 N.", "steps": ["F = 5 kg × 3 m/s².", "F = 15 N.", "Select option D."], "text": "Answer: 15 N\nSteps:\n1. F = 5 kg × 3 m/s².\n2. F = 15 N.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0380", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 5 A. What is its power?", "choices": {"A": "48 W", "B": "72 W", "C": "84 W", "D": "60 W"}, "answer": "Power is 60 W.", "steps": ["P = 12 V × 5 A.", "P = 60 W.", "Select option D."], "text": "Answer: 60 W\nSteps:\n1. P = 12 V × 5 A.\n2. P = 60 W.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0381", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Co je teplotní roztažnost?", "choices": null, "answer": "Zahřáté částice se rozestupují.", "steps": ["Zahřáté částice se rozestupují.", "Odpověď tedy platí: Zahřáté částice se rozestupují."], "text": "Answer: Zahřáté částice se rozestupují.\nSteps:\n1. Zahřáté částice se rozestupují.\n2. Odpověď tedy platí: Zahřáté částice se rozestupují."}
{"id": "phy_0382", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 80 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 8×.", "steps": ["M = di/do.", "M = 80 cm / 10 cm.", "= 8×."], "text": "Answer: Magnification: 8×.\nSteps:\n1. M = di/do.\n2. M = 80 cm / 10 cm.\n3. = 8×."}
{"id": "phy_0383", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 170 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 510 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 170 Hz.", "= 510 Hz."], "text": "Answer: 3rd harmonic: 510 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 170 Hz.\n3. = 510 Hz."}
{"id": "phy_0384", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what traps light?", "choices": {"A": "White dwarf", "B": "Black hole", "C": "Red giant", "D": "Blue note"}, "answer": "The answer is Black hole.", "steps": ["Horizon seals.", "So: Black hole.", "Select option B."], "text": "Answer: Black hole\nSteps:\n1. Horizon seals.\n2. So: Black hole.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0385", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 7 kg se pohybuje 3 m/s. Spočítej jeho hybnost.", "choices": null, "answer": "Hybnost: 21 kg·m/s.", "steps": ["p = m×v.", "p = 7 kg × 3 m/s.", "= 21 kg·m/s."], "text": "Answer: Hybnost: 21 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 7 kg × 3 m/s.\n3. = 21 kg·m/s."}
{"id": "phy_0386", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 20 s. How much charge passes?", "choices": {"A": "80 C", "B": "60 C", "C": "100 C", "D": "120 C"}, "answer": "Charge is 80 C.", "steps": ["Q = 4 A × 20 s.", "Q = 80 C.", "Select option A."], "text": "Answer: 80 C\nSteps:\n1. Q = 4 A × 20 s.\n2. Q = 80 C.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0387", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is entropy?", "choices": null, "answer": "Entropy counts microscopic disorder, always growing in isolated change.", "steps": ["Entropy counts microscopic disorder, always growing in isolated change.", "So the answer stands: Entropy counts microscopic disorder, always growing in isolated change."], "text": "Answer: Entropy counts microscopic disorder, always growing in isolated change.\nSteps:\n1. Entropy counts microscopic disorder, always growing in isolated change.\n2. So the answer stands: Entropy counts microscopic disorder, always growing in isolated change."}
{"id": "phy_0388", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why Brewster's angle?", "choices": null, "answer": "Reflected light polarizes fully at one angle, exploited by photographers.", "steps": ["Reflected light polarizes fully at one angle, exploited by photographers.", "So the answer stands: Reflected light polarizes fully at one angle, exploited by photographers."], "text": "Answer: Reflected light polarizes fully at one angle, exploited by photographers.\nSteps:\n1. Reflected light polarizes fully at one angle, exploited by photographers.\n2. So the answer stands: Reflected light polarizes fully at one angle, exploited by photographers."}
{"id": "phy_0389", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 250 Hz and λ = 2 m. What is its speed?", "choices": {"A": "450 m/s", "B": "550 m/s", "C": "600 m/s", "D": "500 m/s"}, "answer": "Speed is 500 m/s.", "steps": ["v = 250 Hz × 2 m.", "v = 500 m/s.", "Select option D."], "text": "Answer: 500 m/s\nSteps:\n1. v = 250 Hz × 2 m.\n2. v = 500 m/s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0390", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what drags mass?", "choices": {"A": "Corn field", "B": "Mine field", "C": "Higgs field", "D": "Playing field"}, "answer": "The answer is Higgs field.", "steps": ["Found in 2012.", "So: Higgs field.", "Select option C."], "text": "Answer: Higgs field\nSteps:\n1. Found in 2012.\n2. So: Higgs field.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0391", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 10 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 30 kg·m/s.", "steps": ["p = m×v.", "p = 10 kg × 3 m/s.", "= 30 kg·m/s."], "text": "Answer: Momentum: 30 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 10 kg × 3 m/s.\n3. = 30 kg·m/s."}
{"id": "phy_0392", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what links V, I, R?", "choices": {"A": "Hooke's law", "B": "Ohm's law", "C": "Boyle's law", "D": "Snell's law"}, "answer": "The answer is Ohm's law.", "steps": ["V equals IR.", "So: Ohm's law.", "Select option B."], "text": "Answer: Ohm's law\nSteps:\n1. V equals IR.\n2. So: Ohm's law.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0393", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why absolute zero?", "choices": null, "answer": "Motion's minimum forbids colder, and the third law bars ever reaching it.", "steps": ["Motion's minimum forbids colder, and the third law bars ever reaching it.", "So the answer stands: Motion's minimum forbids colder, and the third law bars ever reaching it."], "text": "Answer: Motion's minimum forbids colder, and the third law bars ever reaching it.\nSteps:\n1. Motion's minimum forbids colder, and the third law bars ever reaching it.\n2. So the answer stands: Motion's minimum forbids colder, and the third law bars ever reaching it."}
{"id": "phy_0394", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 19×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 6.3 s.", "steps": ["t = d/c.", "t = 19×10⁸ / 3×10⁸ s.", "= 6.3 s."], "text": "Answer: Time: 6.3 s.\nSteps:\n1. t = d/c.\n2. t = 19×10⁸ / 3×10⁸ s.\n3. = 6.3 s."}
{"id": "phy_0395", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 600 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1800 m/s.", "steps": ["v = f×λ.", "v = 600 Hz × 3 m.", "= 1800 m/s."], "text": "Answer: Speed: 1800 m/s.\nSteps:\n1. v = f×λ.\n2. v = 600 Hz × 3 m.\n3. = 1800 m/s."}
{"id": "phy_0396", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 1600 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "350", "B": "450", "C": "500", "D": "400"}, "answer": "400 atoms remain.", "steps": ["Halve twice: 1600 → 800 → 400.", "Left: 400.", "Select option D."], "text": "Answer: 400\nSteps:\n1. Halve twice: 1600 → 800 → 400.\n2. Left: 400.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0397", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 9 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 18 N.", "steps": ["F = m×a.", "F = 9 kg × 2 m/s².", "= 18 N."], "text": "Answer: Net force: 18 N.\nSteps:\n1. F = m×a.\n2. F = 9 kg × 2 m/s².\n3. = 18 N."}
{"id": "phy_0398", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why transformers?", "choices": null, "answer": "Shared flux scales voltage by turns ratio, shipping power high and safe.", "steps": ["Shared flux scales voltage by turns ratio, shipping power high and safe.", "So the answer stands: Shared flux scales voltage by turns ratio, shipping power high and safe."], "text": "Answer: Shared flux scales voltage by turns ratio, shipping power high and safe.\nSteps:\n1. Shared flux scales voltage by turns ratio, shipping power high and safe.\n2. So the answer stands: Shared flux scales voltage by turns ratio, shipping power high and safe."}
{"id": "phy_0399", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is an ideal gas?", "choices": null, "answer": "Point particles with elastic hits obey pV = nRT simply and usefully.", "steps": ["Point particles with elastic hits obey pV = nRT simply and usefully.", "So the answer stands: Point particles with elastic hits obey pV = nRT simply and usefully."], "text": "Answer: Point particles with elastic hits obey pV = nRT simply and usefully.\nSteps:\n1. Point particles with elastic hits obey pV = nRT simply and usefully.\n2. So the answer stands: Point particles with elastic hits obey pV = nRT simply and usefully."}
{"id": "phy_0400", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Předmět leží 60 cm hluboko ve skle (n = 1,5). Spočítej zdánlivou hloubku.", "choices": null, "answer": "Zdánlivá hloubka: 40 cm.", "steps": ["d' = d/n.", "d' = 60 cm / 1,5.", "= 40 cm."], "text": "Answer: Zdánlivá hloubka: 40 cm.\nSteps:\n1. d' = d/n.\n2. d' = 60 cm / 1,5.\n3. = 40 cm."}
{"id": "phy_0401", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vlna na struně má f = 150 Hz a λ = 2 m. Jaká je její rychlost?", "choices": {"A": "250 m/s", "B": "300 m/s", "C": "350 m/s", "D": "400 m/s"}, "answer": "Rychlost je 300 m/s.", "steps": ["v = 150 Hz × 2 m.", "v = 300 m/s.", "Vyber možnost B."], "text": "Answer: 300 m/s\nSteps:\n1. v = 150 Hz × 2 m.\n2. v = 300 m/s.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0402", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why Schrödinger's cat?", "choices": null, "answer": "It dramatizes superposition at large scale, questioning measurement.", "steps": ["It dramatizes superposition at large scale, questioning measurement.", "So the answer stands: It dramatizes superposition at large scale, questioning measurement."], "text": "Answer: It dramatizes superposition at large scale, questioning measurement.\nSteps:\n1. It dramatizes superposition at large scale, questioning measurement.\n2. So the answer stands: It dramatizes superposition at large scale, questioning measurement."}
{"id": "phy_0403", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 40 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 160 J.", "steps": ["W = F×d.", "W = 40 N × 4 m.", "= 160 J."], "text": "Answer: Work: 160 J.\nSteps:\n1. W = F×d.\n2. W = 40 N × 4 m.\n3. = 160 J."}
{"id": "phy_0404", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Proč Ohmův zákon?", "choices": null, "answer": "U rovná se RI pro rezistory.", "steps": ["U rovná se RI pro rezistory.", "Odpověď tedy platí: U rovná se RI pro rezistory."], "text": "Answer: U rovná se RI pro rezistory.\nSteps:\n1. U rovná se RI pro rezistory.\n2. Odpověď tedy platí: U rovná se RI pro rezistory."}
{"id": "phy_0405", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 8 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 66976 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 8 K.", "= 66976 J."], "text": "Answer: Heat: 66976 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 8 K.\n2. = 66976 J."}
{"id": "phy_0406", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 120 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 80 cm.", "steps": ["d' = d/n.", "d' = 120 cm / 1.5.", "= 80 cm."], "text": "Answer: Apparent depth: 80 cm.\nSteps:\n1. d' = d/n.\n2. d' = 120 cm / 1.5.\n3. = 80 cm."}
{"id": "phy_0407", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is the Doppler effect?", "choices": null, "answer": "Motion shifts heard frequency up approaching, down receding.", "steps": ["Motion shifts heard frequency up approaching, down receding.", "So the answer stands: Motion shifts heard frequency up approaching, down receding."], "text": "Answer: Motion shifts heard frequency up approaching, down receding.\nSteps:\n1. Motion shifts heard frequency up approaching, down receding.\n2. So the answer stands: Motion shifts heard frequency up approaching, down receding."}
{"id": "phy_0408", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 11. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 55.", "steps": ["Pairs: 11×10/2.", "= 110/2.", "= 55."], "text": "Answer: Lines: 55.\nSteps:\n1. Pairs: 11×10/2.\n2. = 110/2.\n3. = 55."}
{"id": "phy_0409", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 130 m in 10 s. What is its speed?", "choices": {"A": "13 m/s", "B": "12 m/s", "C": "14 m/s", "D": "15 m/s"}, "answer": "Speed is 13 m/s.", "steps": ["v = 130 m / 10 s.", "v = 13 m/s.", "Select option A."], "text": "Answer: 13 m/s\nSteps:\n1. v = 130 m / 10 s.\n2. v = 13 m/s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0410", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 8 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 96 V.", "steps": ["V = I×R.", "V = 8 A × 12 Ω.", "= 96 V."], "text": "Answer: Voltage: 96 V.\nSteps:\n1. V = I×R.\n2. V = 8 A × 12 Ω.\n3. = 96 V."}
{"id": "phy_0411", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co nikdy neklesá izolovaně?", "choices": {"A": "entropie", "B": "energie", "C": "hmotnost", "D": "náboj"}, "answer": "Odpověď je entropie.", "steps": ["Druhý zákon vládne.", "Tedy: entropie.", "Vyber možnost A."], "text": "Answer: entropie\nSteps:\n1. Druhý zákon vládne.\n2. Tedy: entropie.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0412", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 90 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 9×.", "steps": ["M = di/do.", "M = 90 cm / 10 cm.", "= 9×."], "text": "Answer: Magnification: 9×.\nSteps:\n1. M = di/do.\n2. M = 90 cm / 10 cm.\n3. = 9×."}
{"id": "phy_0413", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Co je amplituda?", "choices": null, "answer": "Maximální výchylka, určuje hlasitost.", "steps": ["Maximální výchylka, určuje hlasitost.", "Odpověď tedy platí: Maximální výchylka, určuje hlasitost."], "text": "Answer: Maximální výchylka, určuje hlasitost.\nSteps:\n1. Maximální výchylka, určuje hlasitost.\n2. Odpověď tedy platí: Maximální výchylka, určuje hlasitost."}
{"id": "phy_0414", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co se zakřivuje společně?", "choices": {"A": "kosmická loď", "B": "jízdní řád", "C": "pracovní stůl", "D": "časoprostor"}, "answer": "Odpověď je časoprostor.", "steps": ["c pevné pro všechny.", "Tedy: časoprostor.", "Vyber možnost D."], "text": "Answer: časoprostor\nSteps:\n1. c pevné pro všechny.\n2. Tedy: časoprostor.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0415", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 7 m/s. What is its kinetic energy?", "choices": {"A": "42 J", "B": "49 J", "C": "56 J", "D": "63 J"}, "answer": "Kinetic energy is 49 J.", "steps": ["KE = ½×2 kg×(7 m/s)².", "KE = 49 J.", "Select option B."], "text": "Answer: 49 J\nSteps:\n1. KE = ½×2 kg×(7 m/s)².\n2. KE = 49 J.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0416", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 12 s. Compute the energy used.", "choices": null, "answer": "Energy: 1200 J.", "steps": ["E = P×t.", "E = 100 W × 12 s.", "= 1200 J."], "text": "Answer: Energy: 1200 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 12 s.\n3. = 1200 J."}
{"id": "phy_0417", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why Boyle's law?", "choices": null, "answer": "Halving volume doubles pressure at fixed temperature, squeezing gas harder.", "steps": ["Halving volume doubles pressure at fixed temperature, squeezing gas harder.", "So the answer stands: Halving volume doubles pressure at fixed temperature, squeezing gas harder."], "text": "Answer: Halving volume doubles pressure at fixed temperature, squeezing gas harder.\nSteps:\n1. Halving volume doubles pressure at fixed temperature, squeezing gas harder.\n2. So the answer stands: Halving volume doubles pressure at fixed temperature, squeezing gas harder."}
{"id": "phy_0418", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what reflects all inside?", "choices": {"A": "Partial entry", "B": "Gentle exit", "C": "Total internal", "D": "Soft landing"}, "answer": "The answer is Total internal.", "steps": ["Gems sparkle.", "So: Total internal.", "Select option C."], "text": "Answer: Total internal\nSteps:\n1. Gems sparkle.\n2. So: Total internal.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0419", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why sonic boom?", "choices": null, "answer": "Supersonic objects pile waves into one loud shock cone.", "steps": ["Supersonic objects pile waves into one loud shock cone.", "So the answer stands: Supersonic objects pile waves into one loud shock cone."], "text": "Answer: Supersonic objects pile waves into one loud shock cone.\nSteps:\n1. Supersonic objects pile waves into one loud shock cone.\n2. So the answer stands: Supersonic objects pile waves into one loud shock cone."}
{"id": "phy_0420", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 6. How many spectral lines can it emit?", "choices": {"A": "15", "B": "14", "C": "16", "D": "17"}, "answer": "Count: 15.", "steps": ["Pairs: 6×5/2.", "Lines: 15.", "Select option A."], "text": "Answer: 15\nSteps:\n1. Pairs: 6×5/2.\n2. Lines: 15.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0421", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co drží rychlost?", "choices": {"A": "velké tření", "B": "silný vítr", "C": "hlasitý hluk", "D": "nulová výsledná síla"}, "answer": "Odpověď je nulová výsledná síla.", "steps": ["První zákon vládne.", "Tedy: nulová výsledná síla.", "Vyber možnost D."], "text": "Answer: nulová výsledná síla\nSteps:\n1. První zákon vládne.\n2. Tedy: nulová výsledná síla.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0422", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is AC?", "choices": null, "answer": "Alternating current reverses sinusoidally, suiting transformers and long lines.", "steps": ["Alternating current reverses sinusoidally, suiting transformers and long lines.", "So the answer stands: Alternating current reverses sinusoidally, suiting transformers and long lines."], "text": "Answer: Alternating current reverses sinusoidally, suiting transformers and long lines.\nSteps:\n1. Alternating current reverses sinusoidally, suiting transformers and long lines.\n2. So the answer stands: Alternating current reverses sinusoidally, suiting transformers and long lines."}
{"id": "phy_0423", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what obeys pV=nRT?", "choices": {"A": "Real solid", "B": "Cold plasma", "C": "Ideal gas", "D": "Dark matter"}, "answer": "The answer is Ideal gas.", "steps": ["Points collide elastic.", "So: Ideal gas.", "Select option C."], "text": "Answer: Ideal gas\nSteps:\n1. Points collide elastic.\n2. So: Ideal gas.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0424", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co dělí bílé?", "choices": {"A": "hranol", "B": "zrcadlo", "C": "čočka", "D": "stínítko"}, "answer": "Odpověď je hranol.", "steps": ["Barvy rozvějířeny.", "Tedy: hranol.", "Vyber možnost A."], "text": "Answer: hranol\nSteps:\n1. Barvy rozvějířeny.\n2. Tedy: hranol.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0425", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is resonance?", "choices": null, "answer": "Matched driving builds huge oscillation, tuning instruments and bridges.", "steps": ["Matched driving builds huge oscillation, tuning instruments and bridges.", "So the answer stands: Matched driving builds huge oscillation, tuning instruments and bridges."], "text": "Answer: Matched driving builds huge oscillation, tuning instruments and bridges.\nSteps:\n1. Matched driving builds huge oscillation, tuning instruments and bridges.\n2. So the answer stands: Matched driving builds huge oscillation, tuning instruments and bridges."}
{"id": "phy_0426", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is tunnelling?", "choices": null, "answer": "Particles leak through forbidden barriers, powering suns and chips.", "steps": ["Particles leak through forbidden barriers, powering suns and chips.", "So the answer stands: Particles leak through forbidden barriers, powering suns and chips."], "text": "Answer: Particles leak through forbidden barriers, powering suns and chips.\nSteps:\n1. Particles leak through forbidden barriers, powering suns and chips.\n2. So the answer stands: Particles leak through forbidden barriers, powering suns and chips."}
{"id": "phy_0427", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is potential energy?", "choices": null, "answer": "Stored energy like mgh waits to convert, powering falls and springs.", "steps": ["Stored energy like mgh waits to convert, powering falls and springs.", "So the answer stands: Stored energy like mgh waits to convert, powering falls and springs."], "text": "Answer: Stored energy like mgh waits to convert, powering falls and springs.\nSteps:\n1. Stored energy like mgh waits to convert, powering falls and springs.\n2. So the answer stands: Stored energy like mgh waits to convert, powering falls and springs."}
{"id": "phy_0428", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 9 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 243 W.", "steps": ["P = I²×R.", "P = (9 A)² × 3 Ω.", "= 243 W."], "text": "Answer: Power: 243 W.\nSteps:\n1. P = I²×R.\n2. P = (9 A)² × 3 Ω.\n3. = 243 W."}
{"id": "phy_0429", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1200 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 120 W.", "steps": ["P = W/t.", "P = 1200 J / 10 s.", "= 120 W."], "text": "Answer: Power: 120 W.\nSteps:\n1. P = W/t.\n2. P = 1200 J / 10 s.\n3. = 120 W."}
{"id": "phy_0430", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 22×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 7.3 s.", "steps": ["t = d/c.", "t = 22×10⁸ / 3×10⁸ s.", "= 7.3 s."], "text": "Answer: Time: 7.3 s.\nSteps:\n1. t = d/c.\n2. t = 22×10⁸ / 3×10⁸ s.\n3. = 7.3 s."}
{"id": "phy_0431", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 5 Hz. What is its period?", "choices": {"A": "0.2 s", "B": "0.17 s", "C": "0.14 s", "D": "0.25 s"}, "answer": "Period is 0.2 s.", "steps": ["T = 1 / 5 Hz.", "T = 0.2 s.", "Select option A."], "text": "Answer: 0.2 s\nSteps:\n1. T = 1 / 5 Hz.\n2. T = 0.2 s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0432", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Proč E rovná se mc²?", "choices": null, "answer": "Hmotnost je zmrazená energie.", "steps": ["Hmotnost je zmrazená energie.", "Odpověď tedy platí: Hmotnost je zmrazená energie."], "text": "Answer: Hmotnost je zmrazená energie.\nSteps:\n1. Hmotnost je zmrazená energie.\n2. Odpověď tedy platí: Hmotnost je zmrazená energie."}
{"id": "phy_0433", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what opposes sliding?", "choices": {"A": "Gravity", "B": "Inertia", "C": "Friction", "D": "Vacuum"}, "answer": "The answer is Friction.", "steps": ["Surfaces grip.", "So: Friction.", "Select option C."], "text": "Answer: Friction\nSteps:\n1. Surfaces grip.\n2. So: Friction.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0434", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Topidlo 100 W běží po 6 s. Spočítej spotřebovanou energii.", "choices": null, "answer": "Energie: 600 J.", "steps": ["E = P×t.", "E = 100 W × 6 s.", "= 600 J."], "text": "Answer: Energie: 600 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 6 s.\n3. = 600 J."}
{"id": "phy_0435", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 23 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 296 K.", "steps": ["Add 273.", "23 + 273.", "= 296 K."], "text": "Answer: Temperature: 296 K.\nSteps:\n1. Add 273.\n2. 23 + 273.\n3. = 296 K."}
{"id": "phy_0436", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what pipes internet?", "choices": {"A": "Copper bells", "B": "Smoke signals", "C": "Carrier owls", "D": "Fibre optics"}, "answer": "The answer is Fibre optics.", "steps": ["Light guided far.", "So: Fibre optics.", "Select option D."], "text": "Answer: Fibre optics\nSteps:\n1. Light guided far.\n2. So: Fibre optics.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0437", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 10 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 3400 m.", "steps": ["d = v×t.", "d = 340 m/s × 10 s.", "= 3400 m."], "text": "Answer: Distance: 3400 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 10 s.\n3. = 3400 m."}
{"id": "phy_0438", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 10 protons and 11 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 21.", "steps": ["A = Z+N.", "A = 10 + 11.", "= 21."], "text": "Answer: Mass number: 21.\nSteps:\n1. A = Z+N.\n2. A = 10 + 11.\n3. = 21."}
{"id": "phy_0439", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what twists rotations?", "choices": {"A": "Work", "B": "Power", "C": "Energy", "D": "Torque"}, "answer": "The answer is Torque.", "steps": ["Lever arm matters.", "So: Torque.", "Select option D."], "text": "Answer: Torque\nSteps:\n1. Lever arm matters.\n2. So: Torque.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0440", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why RMS values?", "choices": null, "answer": "Root-mean-square matches AC heating to DC, quoting fair 230 V mains.", "steps": ["Root-mean-square matches AC heating to DC, quoting fair 230 V mains.", "So the answer stands: Root-mean-square matches AC heating to DC, quoting fair 230 V mains."], "text": "Answer: Root-mean-square matches AC heating to DC, quoting fair 230 V mains.\nSteps:\n1. Root-mean-square matches AC heating to DC, quoting fair 230 V mains.\n2. So the answer stands: Root-mean-square matches AC heating to DC, quoting fair 230 V mains."}
{"id": "phy_0441", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 23 °C. What is it in kelvin?", "choices": {"A": "295 K", "B": "297 K", "C": "298 K", "D": "296 K"}, "answer": "Temperature is 296 K.", "steps": ["23 °C + 273.", "= 296 K.", "Select option D."], "text": "Answer: 296 K\nSteps:\n1. 23 °C + 273.\n2. = 296 K.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0442", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is scattering?", "choices": null, "answer": "Particles redirect light by size, blue skies from tiny air molecules.", "steps": ["Particles redirect light by size, blue skies from tiny air molecules.", "So the answer stands: Particles redirect light by size, blue skies from tiny air molecules."], "text": "Answer: Particles redirect light by size, blue skies from tiny air molecules.\nSteps:\n1. Particles redirect light by size, blue skies from tiny air molecules.\n2. So the answer stands: Particles redirect light by size, blue skies from tiny air molecules."}
{"id": "phy_0443", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vlna má frekvenci 3 Hz. Jaká je její perioda?", "choices": {"A": "0,25 s", "B": "0,2 s", "C": "0,33 s", "D": "0,5 s"}, "answer": "Perioda je 0,33 s.", "steps": ["T = 1 / 3 Hz.", "T = 0,33 s.", "Vyber možnost C."], "text": "Answer: 0,33 s\nSteps:\n1. T = 1 / 3 Hz.\n2. T = 0,33 s.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0444", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 7200 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 1800.", "steps": ["Halve: 7200 → 3600.", "Halve: 3600 → 1800.", "= 1800."], "text": "Answer: Survivors: 1800.\nSteps:\n1. Halve: 7200 → 3600.\n2. Halve: 3600 → 1800.\n3. = 1800."}
{"id": "phy_0445", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 11 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 33 kg·m/s.", "steps": ["p = m×v.", "p = 11 kg × 3 m/s.", "= 33 kg·m/s."], "text": "Answer: Momentum: 33 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 11 kg × 3 m/s.\n3. = 33 kg·m/s."}
{"id": "phy_0446", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 3 A teče přes 3 Ω. Spočítej ztrátový výkon.", "choices": null, "answer": "Výkon: 27 W.", "steps": ["P = I²×R.", "P = (3 A)² × 3 Ω.", "= 27 W."], "text": "Answer: Výkon: 27 W.\nSteps:\n1. P = I²×R.\n2. P = (3 A)² × 3 Ω.\n3. = 27 W."}
{"id": "phy_0447", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 5 K? (c = 4186 J/(kg·K))", "choices": {"A": "20930 J", "B": "16744 J", "C": "25116 J", "D": "29302 J"}, "answer": "Heat needed is 20930 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 5 K.", "Q = 20930 J.", "Select option A."], "text": "Answer: 20930 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 5 K.\n2. Q = 20930 J.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0448", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 135 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 90 cm.", "steps": ["d' = d/n.", "d' = 135 cm / 1.5.", "= 90 cm."], "text": "Answer: Apparent depth: 90 cm.\nSteps:\n1. d' = d/n.\n2. d' = 135 cm / 1.5.\n3. = 90 cm."}
{"id": "phy_0449", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Proč perioda?", "choices": null, "answer": "Je sekund na cyklus, převrácená frekvence.", "steps": ["Je sekund na cyklus, převrácená frekvence.", "Odpověď tedy platí: Je sekund na cyklus, převrácená frekvence."], "text": "Answer: Je sekund na cyklus, převrácená frekvence.\nSteps:\n1. Je sekund na cyklus, převrácená frekvence.\n2. Odpověď tedy platí: Je sekund na cyklus, převrácená frekvence."}
{"id": "phy_0450", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 5 protons and 5 neutrons. What is its mass number?", "choices": {"A": "9", "B": "10", "C": "11", "D": "12"}, "answer": "Mass number is 10.", "steps": ["A = 5 + 5.", "A = 10.", "Select option B."], "text": "Answer: 10\nSteps:\n1. A = 5 + 5.\n2. A = 10.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0451", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 10 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 20 N.", "steps": ["F = m×a.", "F = 10 kg × 2 m/s².", "= 20 N."], "text": "Answer: Net force: 20 N.\nSteps:\n1. F = m×a.\n2. F = 10 kg × 2 m/s².\n3. = 20 N."}
{"id": "phy_0452", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what unifies four laws?", "choices": {"A": "Newton's laws", "B": "Kepler's laws", "C": "Maxwell's equations", "D": "Ohm's laws"}, "answer": "The answer is Maxwell's equations.", "steps": ["Light predicted.", "So: Maxwell's equations.", "Select option C."], "text": "Answer: Maxwell's equations\nSteps:\n1. Light predicted.\n2. So: Maxwell's equations.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0453", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is Charles's law?", "choices": null, "answer": "Volume grows with Kelvin temperature at fixed pressure, expanding balloons.", "steps": ["Volume grows with Kelvin temperature at fixed pressure, expanding balloons.", "So the answer stands: Volume grows with Kelvin temperature at fixed pressure, expanding balloons."], "text": "Answer: Volume grows with Kelvin temperature at fixed pressure, expanding balloons.\nSteps:\n1. Volume grows with Kelvin temperature at fixed pressure, expanding balloons.\n2. So the answer stands: Volume grows with Kelvin temperature at fixed pressure, expanding balloons."}
{"id": "phy_0454", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Obraz vzniká 30 cm od čočky, předmět v 10 cm. Jaké je zvětšení?", "choices": {"A": "2×", "B": "3×", "C": "4×", "D": "5×"}, "answer": "Zvětšení je 3×.", "steps": ["M = 30 cm / 10 cm.", "M = 3×.", "Vyber možnost B."], "text": "Answer: 3×\nSteps:\n1. M = 30 cm / 10 cm.\n2. M = 3×.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0455", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 140 Hz. What is its 3rd harmonic?", "choices": {"A": "390 Hz", "B": "420 Hz", "C": "450 Hz", "D": "480 Hz"}, "answer": "3rd harmonic is 420 Hz.", "steps": ["f3 = 3 × 140 Hz.", "f3 = 420 Hz.", "Select option B."], "text": "Answer: 420 Hz\nSteps:\n1. f3 = 3 × 140 Hz.\n2. f3 = 420 Hz.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0456", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 12. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 66.", "steps": ["Pairs: 12×11/2.", "= 132/2.", "= 66."], "text": "Answer: Lines: 66.\nSteps:\n1. Pairs: 12×11/2.\n2. = 132/2.\n3. = 66."}
{"id": "phy_0457", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 45 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 180 J.", "steps": ["W = F×d.", "W = 45 N × 4 m.", "= 180 J."], "text": "Answer: Work: 180 J.\nSteps:\n1. W = F×d.\n2. W = 45 N × 4 m.\n3. = 180 J."}
{"id": "phy_0458", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 3 A teče přes 12 Ω. Spočítej napětí.", "choices": null, "answer": "Napětí: 36 V.", "steps": ["U = I×R.", "U = 3 A × 12 Ω.", "= 36 V."], "text": "Answer: Napětí: 36 V.\nSteps:\n1. U = I×R.\n2. U = 3 A × 12 Ω.\n3. = 36 V."}
{"id": "phy_0459", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Proč vedení tepla?", "choices": null, "answer": "Srážející se částice předávají energii.", "steps": ["Srážející se částice předávají energii.", "Odpověď tedy platí: Srážející se částice předávají energii."], "text": "Answer: Srážející se částice předávají energii.\nSteps:\n1. Srážející se částice předávají energii.\n2. Odpověď tedy platí: Srážející se částice předávají energii."}
{"id": "phy_0460", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 100 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 10×.", "steps": ["M = di/do.", "M = 100 cm / 10 cm.", "= 10×."], "text": "Answer: Magnification: 10×.\nSteps:\n1. M = di/do.\n2. M = 100 cm / 10 cm.\n3. = 10×."}
{"id": "phy_0461", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 180 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 540 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 180 Hz.", "= 540 Hz."], "text": "Answer: 3rd harmonic: 540 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 180 Hz.\n3. = 540 Hz."}
{"id": "phy_0462", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 11 protons and 12 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 23.", "steps": ["A = Z+N.", "A = 11 + 12.", "= 23."], "text": "Answer: Mass number: 23.\nSteps:\n1. A = Z+N.\n2. A = 11 + 12.\n3. = 23."}
{"id": "phy_0463", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 6 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "18 N", "B": "15 N", "C": "21 N", "D": "24 N"}, "answer": "Net force is 18 N.", "steps": ["F = 6 kg × 3 m/s².", "F = 18 N.", "Select option A."], "text": "Answer: 18 N\nSteps:\n1. F = 6 kg × 3 m/s².\n2. F = 18 N.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0464", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 5 A flows through 5 Ω. What is the voltage?", "choices": {"A": "20 V", "B": "30 V", "C": "35 V", "D": "25 V"}, "answer": "Voltage is 25 V.", "steps": ["V = 5 A × 5 Ω.", "V = 25 V.", "Select option D."], "text": "Answer: 25 V\nSteps:\n1. V = 5 A × 5 Ω.\n2. V = 25 V.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0465", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 9 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 75348 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 9 K.", "= 75348 J."], "text": "Answer: Heat: 75348 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 9 K.\n2. = 75348 J."}
{"id": "phy_0466", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 25×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 8.3 s.", "steps": ["t = d/c.", "t = 25×10⁸ / 3×10⁸ s.", "= 8.3 s."], "text": "Answer: Time: 8.3 s.\nSteps:\n1. t = d/c.\n2. t = 25×10⁸ / 3×10⁸ s.\n3. = 8.3 s."}
{"id": "phy_0467", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 650 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 1950 m/s.", "steps": ["v = f×λ.", "v = 650 Hz × 3 m.", "= 1950 m/s."], "text": "Answer: Speed: 1950 m/s.\nSteps:\n1. v = f×λ.\n2. v = 650 Hz × 3 m.\n3. = 1950 m/s."}
{"id": "phy_0468", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what blends till measured?", "choices": {"A": "Superscription", "B": "Superstition", "C": "Superposition", "D": "Supervision"}, "answer": "The answer is Superposition.", "steps": ["One outcome picked.", "So: Superposition.", "Select option C."], "text": "Answer: Superposition\nSteps:\n1. One outcome picked.\n2. So: Superposition.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0469", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 12 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 36 kg·m/s.", "steps": ["p = m×v.", "p = 12 kg × 3 m/s.", "= 36 kg·m/s."], "text": "Answer: Momentum: 36 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 12 kg × 3 m/s.\n3. = 36 kg·m/s."}
{"id": "phy_0470", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 6 A. What is its power?", "choices": {"A": "72 W", "B": "60 W", "C": "84 W", "D": "96 W"}, "answer": "Power is 72 W.", "steps": ["P = 12 V × 6 A.", "P = 72 W.", "Select option A."], "text": "Answer: 72 W\nSteps:\n1. P = 12 V × 6 A.\n2. P = 72 W.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0471", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Pokojová teplota je 21 °C. Kolik je to kelvinů?", "choices": {"A": "293 K", "B": "294 K", "C": "295 K", "D": "296 K"}, "answer": "Teplota je 294 K.", "steps": ["21 °C + 273.", "= 294 K.", "Vyber možnost B."], "text": "Answer: 294 K\nSteps:\n1. 21 °C + 273.\n2. = 294 K.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0472", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Obraz vzniká 50 cm od čočky, předmět v 10 cm. Spočítej zvětšení.", "choices": null, "answer": "Zvětšení: 5×.", "steps": ["M = di/do.", "M = 50 cm / 10 cm.", "= 5×."], "text": "Answer: Zvětšení: 5×.\nSteps:\n1. M = di/do.\n2. M = 50 cm / 10 cm.\n3. = 5×."}
{"id": "phy_0473", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why standing waves?", "choices": null, "answer": "Reflected waves lock into fixed nodes, forming musical notes.", "steps": ["Reflected waves lock into fixed nodes, forming musical notes.", "So the answer stands: Reflected waves lock into fixed nodes, forming musical notes."], "text": "Answer: Reflected waves lock into fixed nodes, forming musical notes.\nSteps:\n1. Reflected waves lock into fixed nodes, forming musical notes.\n2. So the answer stands: Reflected waves lock into fixed nodes, forming musical notes."}
{"id": "phy_0474", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Jádro má 4 protonů a 5 neutronů. Spočítej jeho nukleonové číslo.", "choices": null, "answer": "Nukleonové číslo: 9.", "steps": ["A = Z+N.", "A = 4 + 5.", "= 9."], "text": "Answer: Nukleonové číslo: 9.\nSteps:\n1. A = Z+N.\n2. A = 4 + 5.\n3. = 9."}
{"id": "phy_0475", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 140 m in 10 s. What is its speed?", "choices": {"A": "13 m/s", "B": "14 m/s", "C": "15 m/s", "D": "16 m/s"}, "answer": "Speed is 14 m/s.", "steps": ["v = 140 m / 10 s.", "v = 14 m/s.", "Select option B."], "text": "Answer: 14 m/s\nSteps:\n1. v = 140 m / 10 s.\n2. v = 14 m/s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0476", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 9 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 108 V.", "steps": ["V = I×R.", "V = 9 A × 12 Ω.", "= 108 V."], "text": "Answer: Voltage: 108 V.\nSteps:\n1. V = I×R.\n2. V = 9 A × 12 Ω.\n3. = 108 V."}
{"id": "phy_0477", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why Avogadro's number?", "choices": null, "answer": "One mole holds 6.02e23 particles, bridging atoms to grams.", "steps": ["One mole holds 6.02e23 particles, bridging atoms to grams.", "So the answer stands: One mole holds 6.02e23 particles, bridging atoms to grams."], "text": "Answer: One mole holds 6.02e23 particles, bridging atoms to grams.\nSteps:\n1. One mole holds 6.02e23 particles, bridging atoms to grams.\n2. So the answer stands: One mole holds 6.02e23 particles, bridging atoms to grams."}
{"id": "phy_0478", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 150 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 100 cm.", "steps": ["d' = d/n.", "d' = 150 cm / 1.5.", "= 100 cm."], "text": "Answer: Apparent depth: 100 cm.\nSteps:\n1. d' = d/n.\n2. d' = 150 cm / 1.5.\n3. = 100 cm."}
{"id": "phy_0479", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What are harmonics?", "choices": null, "answer": "Integer multiples of the fundamental ring together, colouring timbre.", "steps": ["Integer multiples of the fundamental ring together, colouring timbre.", "So the answer stands: Integer multiples of the fundamental ring together, colouring timbre."], "text": "Answer: Integer multiples of the fundamental ring together, colouring timbre.\nSteps:\n1. Integer multiples of the fundamental ring together, colouring timbre.\n2. So the answer stands: Integer multiples of the fundamental ring together, colouring timbre."}
{"id": "phy_0480", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why lasers quantum?", "choices": null, "answer": "Stimulated emission clones photons identically, a pure quantum device.", "steps": ["Stimulated emission clones photons identically, a pure quantum device.", "So the answer stands: Stimulated emission clones photons identically, a pure quantum device."], "text": "Answer: Stimulated emission clones photons identically, a pure quantum device.\nSteps:\n1. Stimulated emission clones photons identically, a pure quantum device.\n2. So the answer stands: Stimulated emission clones photons identically, a pure quantum device."}
{"id": "phy_0481", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 11 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 22 N.", "steps": ["F = m×a.", "F = 11 kg × 2 m/s².", "= 22 N."], "text": "Answer: Net force: 22 N.\nSteps:\n1. F = m×a.\n2. F = 11 kg × 2 m/s².\n3. = 22 N."}
{"id": "phy_0482", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is impedance?", "choices": null, "answer": "Impedance extends resistance to AC with phase, combining R, L, and C.", "steps": ["Impedance extends resistance to AC with phase, combining R, L, and C.", "So the answer stands: Impedance extends resistance to AC with phase, combining R, L, and C."], "text": "Answer: Impedance extends resistance to AC with phase, combining R, L, and C.\nSteps:\n1. Impedance extends resistance to AC with phase, combining R, L, and C.\n2. So the answer stands: Impedance extends resistance to AC with phase, combining R, L, and C."}
{"id": "phy_0483", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1300 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 130 W.", "steps": ["P = W/t.", "P = 1300 J / 10 s.", "= 130 W."], "text": "Answer: Power: 130 W.\nSteps:\n1. P = W/t.\n2. P = 1300 J / 10 s.\n3. = 130 W."}
{"id": "phy_0484", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 110 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 11×.", "steps": ["M = di/do.", "M = 110 cm / 10 cm.", "= 11×."], "text": "Answer: Magnification: 11×.\nSteps:\n1. M = di/do.\n2. M = 110 cm / 10 cm.\n3. = 11×."}
{"id": "phy_0485", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why beats?", "choices": null, "answer": "Near frequencies alternate loud and soft at their difference rate.", "steps": ["Near frequencies alternate loud and soft at their difference rate.", "So the answer stands: Near frequencies alternate loud and soft at their difference rate."], "text": "Answer: Near frequencies alternate loud and soft at their difference rate.\nSteps:\n1. Near frequencies alternate loud and soft at their difference rate.\n2. So the answer stands: Near frequencies alternate loud and soft at their difference rate."}
{"id": "phy_0486", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 8000 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 2000.", "steps": ["Halve: 8000 → 4000.", "Halve: 4000 → 2000.", "= 2000."], "text": "Answer: Survivors: 2000.\nSteps:\n1. Halve: 8000 → 4000.\n2. Halve: 4000 → 2000.\n3. = 2000."}
{"id": "phy_0487", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why conserve energy?", "choices": null, "answer": "Isolated total energy never changes form-sum, so accounting always balances.", "steps": ["Isolated total energy never changes form-sum, so accounting always balances.", "So the answer stands: Isolated total energy never changes form-sum, so accounting always balances."], "text": "Answer: Isolated total energy never changes form-sum, so accounting always balances.\nSteps:\n1. Isolated total energy never changes form-sum, so accounting always balances.\n2. So the answer stands: Isolated total energy never changes form-sum, so accounting always balances."}
{"id": "phy_0488", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 25 s. How much charge passes?", "choices": {"A": "80 C", "B": "100 C", "C": "120 C", "D": "140 C"}, "answer": "Charge is 100 C.", "steps": ["Q = 4 A × 25 s.", "Q = 100 C.", "Select option B."], "text": "Answer: 100 C\nSteps:\n1. Q = 4 A × 25 s.\n2. Q = 100 C.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0489", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 24 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 297 K.", "steps": ["Add 273.", "24 + 273.", "= 297 K."], "text": "Answer: Temperature: 297 K.\nSteps:\n1. Add 273.\n2. 24 + 273.\n3. = 297 K."}
{"id": "phy_0490", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 60 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "6×", "B": "5×", "C": "7×", "D": "8×"}, "answer": "Magnification is 6×.", "steps": ["M = 60 cm / 10 cm.", "M = 6×.", "Select option A."], "text": "Answer: 6×\nSteps:\n1. M = 60 cm / 10 cm.\n2. M = 6×.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0491", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is the decibel?", "choices": null, "answer": "Log loudness scale where +10 dB means ten times the power.", "steps": ["Log loudness scale where +10 dB means ten times the power.", "So the answer stands: Log loudness scale where +10 dB means ten times the power."], "text": "Answer: Log loudness scale where +10 dB means ten times the power.\nSteps:\n1. Log loudness scale where +10 dB means ten times the power.\n2. So the answer stands: Log loudness scale where +10 dB means ten times the power."}
{"id": "phy_0492", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 13. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 78.", "steps": ["Pairs: 13×12/2.", "= 156/2.", "= 78."], "text": "Answer: Lines: 78.\nSteps:\n1. Pairs: 13×12/2.\n2. = 156/2.\n3. = 78."}
{"id": "phy_0493", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is power?", "choices": null, "answer": "Power is energy per time in watts, rating how fast work gets done.", "steps": ["Power is energy per time in watts, rating how fast work gets done.", "So the answer stands: Power is energy per time in watts, rating how fast work gets done."], "text": "Answer: Power is energy per time in watts, rating how fast work gets done.\nSteps:\n1. Power is energy per time in watts, rating how fast work gets done.\n2. So the answer stands: Power is energy per time in watts, rating how fast work gets done."}
{"id": "phy_0494", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 13 s. Compute the energy used.", "choices": null, "answer": "Energy: 1300 J.", "steps": ["E = P×t.", "E = 100 W × 13 s.", "= 1300 J."], "text": "Answer: Energy: 1300 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 13 s.\n3. = 1300 J."}
{"id": "phy_0495", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Co je první zákon?", "choices": null, "answer": "Zachování energie pro teplo a práci.", "steps": ["Zachování energie pro teplo a práci.", "Odpověď tedy platí: Zachování energie pro teplo a práci."], "text": "Answer: Zachování energie pro teplo a práci.\nSteps:\n1. Zachování energie pro teplo a práci.\n2. Odpověď tedy platí: Zachování energie pro teplo a práci."}
{"id": "phy_0496", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Světlo letí 10×10⁸ m. Spočítej dobu letu. (c = 3×10⁸ m/s)", "choices": null, "answer": "Čas: 3,3 s.", "steps": ["t = d/c.", "t = 10×10⁸ / 3×10⁸ s.", "= 3,3 s."], "text": "Answer: Čas: 3,3 s.\nSteps:\n1. t = d/c.\n2. t = 10×10⁸ / 3×10⁸ s.\n3. = 3,3 s."}
{"id": "phy_0497", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Vlna na struně má f = 300 Hz a λ = 3 m. Spočítej její rychlost.", "choices": null, "answer": "Rychlost: 900 m/s.", "steps": ["v = f×λ.", "v = 300 Hz × 3 m.", "= 900 m/s."], "text": "Answer: Rychlost: 900 m/s.\nSteps:\n1. v = f×λ.\n2. v = 300 Hz × 3 m.\n3. = 900 m/s."}
{"id": "phy_0498", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Co je černá díra?", "choices": null, "answer": "Hmota stlačená za horizontem chytí i světlo.", "steps": ["Hmota stlačená za horizontem chytí i světlo.", "Odpověď tedy platí: Hmota stlačená za horizontem chytí i světlo."], "text": "Answer: Hmota stlačená za horizontem chytí i světlo.\nSteps:\n1. Hmota stlačená za horizontem chytí i světlo.\n2. Odpověď tedy platí: Hmota stlačená za horizontem chytí i světlo."}
{"id": "phy_0499", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 50 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 200 J.", "steps": ["W = F×d.", "W = 50 N × 4 m.", "= 200 J."], "text": "Answer: Work: 200 J.\nSteps:\n1. W = F×d.\n2. W = 50 N × 4 m.\n3. = 200 J."}
{"id": "phy_0500", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Topidlo 100 W běží po 7 s. Spočítej spotřebovanou energii.", "choices": null, "answer": "Energie: 700 J.", "steps": ["E = P×t.", "E = 100 W × 7 s.", "= 700 J."], "text": "Answer: Energie: 700 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 7 s.\n3. = 700 J."}
{"id": "phy_0501", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is latent heat?", "choices": null, "answer": "Melting and boiling absorb energy without temperature change, hiding heat in bonds.", "steps": ["Melting and boiling absorb energy without temperature change, hiding heat in bonds.", "So the answer stands: Melting and boiling absorb energy without temperature change, hiding heat in bonds."], "text": "Answer: Melting and boiling absorb energy without temperature change, hiding heat in bonds.\nSteps:\n1. Melting and boiling absorb energy without temperature change, hiding heat in bonds.\n2. So the answer stands: Melting and boiling absorb energy without temperature change, hiding heat in bonds."}
{"id": "phy_0502", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 28×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 9.3 s.", "steps": ["t = d/c.", "t = 28×10⁸ / 3×10⁸ s.", "= 9.3 s."], "text": "Answer: Time: 9.3 s.\nSteps:\n1. t = d/c.\n2. t = 28×10⁸ / 3×10⁸ s.\n3. = 9.3 s."}
{"id": "phy_0503", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 11 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 3740 m.", "steps": ["d = v×t.", "d = 340 m/s × 11 s.", "= 3740 m."], "text": "Answer: Distance: 3740 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 11 s.\n3. = 3740 m."}
{"id": "phy_0504", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 12 protons and 13 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 25.", "steps": ["A = Z+N.", "A = 12 + 13.", "= 25."], "text": "Answer: Mass number: 25.\nSteps:\n1. A = Z+N.\n2. A = 12 + 13.\n3. = 25."}
{"id": "phy_0505", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Co je práce?", "choices": null, "answer": "Práce je síla krát dráha, měří se v joulech.", "steps": ["Práce je síla krát dráha, měří se v joulech.", "Odpověď tedy platí: Práce je síla krát dráha, měří se v joulech."], "text": "Answer: Práce je síla krát dráha, měří se v joulech.\nSteps:\n1. Práce je síla krát dráha, měří se v joulech.\n2. Odpověď tedy platí: Práce je síla krát dráha, měří se v joulech."}
{"id": "phy_0506", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why resonance circuits?", "choices": null, "answer": "LC tunes to one frequency selectively, picking radio stations cleanly.", "steps": ["LC tunes to one frequency selectively, picking radio stations cleanly.", "So the answer stands: LC tunes to one frequency selectively, picking radio stations cleanly."], "text": "Answer: LC tunes to one frequency selectively, picking radio stations cleanly.\nSteps:\n1. LC tunes to one frequency selectively, picking radio stations cleanly.\n2. So the answer stands: LC tunes to one frequency selectively, picking radio stations cleanly."}
{"id": "phy_0507", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 500 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "40%", "B": "50%", "C": "60%", "D": "70%"}, "answer": "Efficiency is 50%.", "steps": ["500 J / 1000 J.", "= 50%.", "Select option B."], "text": "Answer: 50%\nSteps:\n1. 500 J / 1000 J.\n2. = 50%.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0508", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 15×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "6 s", "B": "5 s", "C": "7 s", "D": "4 s"}, "answer": "Time is 5 s.", "steps": ["t = 15×10⁸ m / 3×10⁸ m/s.", "t = 5 s.", "Select option B."], "text": "Answer: 5 s\nSteps:\n1. t = 15×10⁸ m / 3×10⁸ m/s.\n2. t = 5 s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0509", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 190 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 570 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 190 Hz.", "= 570 Hz."], "text": "Answer: 3rd harmonic: 570 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 190 Hz.\n3. = 570 Hz."}
{"id": "phy_0510", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is the photoelectric effect?", "choices": null, "answer": "Photons eject electrons past threshold frequency only.", "steps": ["Photons eject electrons past threshold frequency only.", "So the answer stands: Photons eject electrons past threshold frequency only."], "text": "Answer: Photons eject electrons past threshold frequency only.\nSteps:\n1. Photons eject electrons past threshold frequency only.\n2. So the answer stands: Photons eject electrons past threshold frequency only."}
{"id": "phy_0511", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 8 m/s. What is its kinetic energy?", "choices": {"A": "56 J", "B": "72 J", "C": "64 J", "D": "80 J"}, "answer": "Kinetic energy is 64 J.", "steps": ["KE = ½×2 kg×(8 m/s)².", "KE = 64 J.", "Select option C."], "text": "Answer: 64 J\nSteps:\n1. KE = ½×2 kg×(8 m/s)².\n2. KE = 64 J.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0512", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what stores per volt?", "choices": {"A": "Resistor", "B": "Inductor", "C": "Capacitor", "D": "Diode"}, "answer": "The answer is Capacitor.", "steps": ["Plates hold charge.", "So: Capacitor.", "Select option C."], "text": "Answer: Capacitor\nSteps:\n1. Plates hold charge.\n2. So: Capacitor.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0513", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 10 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 83720 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 10 K.", "= 83720 J."], "text": "Answer: Heat: 83720 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 10 K.\n2. = 83720 J."}
{"id": "phy_0514", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Předmět leží 75 cm hluboko ve skle (n = 1,5). Spočítej zdánlivou hloubku.", "choices": null, "answer": "Zdánlivá hloubka: 50 cm.", "steps": ["d' = d/n.", "d' = 75 cm / 1,5.", "= 50 cm."], "text": "Answer: Zdánlivá hloubka: 50 cm.\nSteps:\n1. d' = d/n.\n2. d' = 75 cm / 1,5.\n3. = 50 cm."}
{"id": "phy_0515", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Základ struny je 120 Hz. Jaká je její 3. harmonická?", "choices": {"A": "330 Hz", "B": "390 Hz", "C": "420 Hz", "D": "360 Hz"}, "answer": "3. harmonická je 360 Hz.", "steps": ["f3 = 3 × 120 Hz.", "f3 = 360 Hz.", "Vyber možnost D."], "text": "Answer: 360 Hz\nSteps:\n1. f3 = 3 × 120 Hz.\n2. f3 = 360 Hz.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0516", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Vzorek 2400 atomů projde 2 poločasy. Spočítej přeživší.", "choices": null, "answer": "Přeživší: 600.", "steps": ["Půl: 2400 → 1200.", "Půl: 1200 → 600.", "= 600."], "text": "Answer: Přeživší: 600.\nSteps:\n1. Půl: 2400 → 1200.\n2. Půl: 1200 → 600.\n3. = 600."}
{"id": "phy_0517", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what traces parabolas?", "choices": {"A": "Orbits", "B": "Pendulums", "C": "Gears", "D": "Projectiles"}, "answer": "The answer is Projectiles.", "steps": ["Gravity bends paths.", "So: Projectiles.", "Select option D."], "text": "Answer: Projectiles\nSteps:\n1. Gravity bends paths.\n2. So: Projectiles.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0518", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What are Maxwell's equations?", "choices": null, "answer": "Four laws unify electricity and magnetism, predicting light as waves.", "steps": ["Four laws unify electricity and magnetism, predicting light as waves.", "So the answer stands: Four laws unify electricity and magnetism, predicting light as waves."], "text": "Answer: Four laws unify electricity and magnetism, predicting light as waves.\nSteps:\n1. Four laws unify electricity and magnetism, predicting light as waves.\n2. So the answer stands: Four laws unify electricity and magnetism, predicting light as waves."}
{"id": "phy_0519", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Motor vykoná 600 J práce za 10 s. Spočítej jeho výkon.", "choices": null, "answer": "Výkon: 60 W.", "steps": ["P = W/t.", "P = 600 J / 10 s.", "= 60 W."], "text": "Answer: Výkon: 60 W.\nSteps:\n1. P = W/t.\n2. P = 600 J / 10 s.\n3. = 60 W."}
{"id": "phy_0520", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 90 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "55 cm", "B": "65 cm", "C": "60 cm", "D": "70 cm"}, "answer": "Apparent depth is 60 cm.", "steps": ["d' = 90 cm / 1.5.", "d' = 60 cm.", "Select option C."], "text": "Answer: 60 cm\nSteps:\n1. d' = 90 cm / 1.5.\n2. d' = 60 cm.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0521", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what shifts with motion?", "choices": {"A": "Static volume", "B": "Calm tempo", "C": "Doppler pitch", "D": "Fixed key"}, "answer": "The answer is Doppler pitch.", "steps": ["Approach raises.", "So: Doppler pitch.", "Select option C."], "text": "Answer: Doppler pitch\nSteps:\n1. Approach raises.\n2. So: Doppler pitch.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0522", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co dělí těžké?", "choices": {"A": "štěpení", "B": "fúze", "C": "móda", "D": "fikce"}, "answer": "Odpověď je štěpení.", "steps": ["Reaktory řetězeny.", "Tedy: štěpení.", "Vyber možnost A."], "text": "Answer: štěpení\nSteps:\n1. Reaktory řetězeny.\n2. Tedy: štěpení.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0523", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why momentum?", "choices": null, "answer": "Momentum mv persists through collisions, predicting outcomes via conservation.", "steps": ["Momentum mv persists through collisions, predicting outcomes via conservation.", "So the answer stands: Momentum mv persists through collisions, predicting outcomes via conservation."], "text": "Answer: Momentum mv persists through collisions, predicting outcomes via conservation.\nSteps:\n1. Momentum mv persists through collisions, predicting outcomes via conservation.\n2. So the answer stands: Momentum mv persists through collisions, predicting outcomes via conservation."}
{"id": "phy_0524", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 10 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 300 W.", "steps": ["P = I²×R.", "P = (10 A)² × 3 Ω.", "= 300 W."], "text": "Answer: Power: 300 W.\nSteps:\n1. P = I²×R.\n2. P = (10 A)² × 3 Ω.\n3. = 300 W."}
{"id": "phy_0525", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1400 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 140 W.", "steps": ["P = W/t.", "P = 1400 J / 10 s.", "= 140 W."], "text": "Answer: Power: 140 W.\nSteps:\n1. P = W/t.\n2. P = 1400 J / 10 s.\n3. = 140 W."}
{"id": "phy_0526", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 165 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 110 cm.", "steps": ["d' = d/n.", "d' = 165 cm / 1.5.", "= 110 cm."], "text": "Answer: Apparent depth: 110 cm.\nSteps:\n1. d' = d/n.\n2. d' = 165 cm / 1.5.\n3. = 110 cm."}
{"id": "phy_0527", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what erases rumble?", "choices": {"A": "More bass", "B": "Less treble", "C": "Pure luck", "D": "Anti-phase"}, "answer": "The answer is Anti-phase.", "steps": ["Quiet engineered.", "So: Anti-phase.", "Select option D."], "text": "Answer: Anti-phase\nSteps:\n1. Quiet engineered.\n2. So: Anti-phase.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0528", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what burns on contact?", "choices": {"A": "Dark matter", "B": "Gray area", "C": "Cold feet", "D": "Antimatter"}, "answer": "The answer is Antimatter.", "steps": ["Gamma flashed.", "So: Antimatter.", "Select option D."], "text": "Answer: Antimatter\nSteps:\n1. Gamma flashed.\n2. So: Antimatter.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0529", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is impulse?", "choices": null, "answer": "Impulse is force times time, equal to momentum change in every shove.", "steps": ["Impulse is force times time, equal to momentum change in every shove.", "So the answer stands: Impulse is force times time, equal to momentum change in every shove."], "text": "Answer: Impulse is force times time, equal to momentum change in every shove.\nSteps:\n1. Impulse is force times time, equal to momentum change in every shove.\n2. So the answer stands: Impulse is force times time, equal to momentum change in every shove."}
{"id": "phy_0530", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what passes one way?", "choices": {"A": "Wire", "B": "Fuse", "C": "Switch", "D": "Diode"}, "answer": "The answer is Diode.", "steps": ["AC rectified.", "So: Diode.", "Select option D."], "text": "Answer: Diode\nSteps:\n1. AC rectified.\n2. So: Diode.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0531", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Teplota je 17 °C. Převeď ji na kelviny.", "choices": null, "answer": "Teplota: 290 K.", "steps": ["Přičti 273.", "17 + 273.", "= 290 K."], "text": "Answer: Teplota: 290 K.\nSteps:\n1. Přičti 273.\n2. 17 + 273.\n3. = 290 K."}
{"id": "phy_0532", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 120 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 12×.", "steps": ["M = di/do.", "M = 120 cm / 10 cm.", "= 12×."], "text": "Answer: Magnification: 12×.\nSteps:\n1. M = di/do.\n2. M = 120 cm / 10 cm.\n3. = 12×."}
{"id": "phy_0533", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 300 Hz and λ = 2 m. What is its speed?", "choices": {"A": "600 m/s", "B": "550 m/s", "C": "650 m/s", "D": "700 m/s"}, "answer": "Speed is 600 m/s.", "steps": ["v = 300 Hz × 2 m.", "v = 600 m/s.", "Select option A."], "text": "Answer: 600 m/s\nSteps:\n1. v = 300 Hz × 2 m.\n2. v = 600 m/s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0534", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why solar cells?", "choices": null, "answer": "Junction fields sweep freed charges into current efficiently.", "steps": ["Junction fields sweep freed charges into current efficiently.", "So the answer stands: Junction fields sweep freed charges into current efficiently."], "text": "Answer: Junction fields sweep freed charges into current efficiently.\nSteps:\n1. Junction fields sweep freed charges into current efficiently.\n2. So the answer stands: Junction fields sweep freed charges into current efficiently."}
{"id": "phy_0535", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 13 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 39 kg·m/s.", "steps": ["p = m×v.", "p = 13 kg × 3 m/s.", "= 39 kg·m/s."], "text": "Answer: Momentum: 39 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 13 kg × 3 m/s.\n3. = 39 kg·m/s."}
{"id": "phy_0536", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 10 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 120 V.", "steps": ["V = I×R.", "V = 10 A × 12 Ω.", "= 120 V."], "text": "Answer: Voltage: 120 V.\nSteps:\n1. V = I×R.\n2. V = 10 A × 12 Ω.\n3. = 120 V."}
{"id": "phy_0537", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what buffers climate?", "choices": {"A": "Iron's mass", "B": "Sand's color", "C": "Water's heat", "D": "Air's smell"}, "answer": "The answer is Water's heat.", "steps": ["High capacity held.", "So: Water's heat.", "Select option C."], "text": "Answer: Water's heat\nSteps:\n1. High capacity held.\n2. So: Water's heat.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0538", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Světlo letí 6×10⁸ m. Kolik sekund to trvá? (c = 3×10⁸ m/s)", "choices": {"A": "3 s", "B": "4 s", "C": "2 s", "D": "1 s"}, "answer": "Čas je 2 s.", "steps": ["t = 6×10⁸ m / 3×10⁸ m/s.", "t = 2 s.", "Vyber možnost C."], "text": "Answer: 2 s\nSteps:\n1. t = 6×10⁸ m / 3×10⁸ m/s.\n2. t = 2 s.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0539", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Co je zvuk?", "choices": null, "answer": "Tlakové vlny vzduchu slyšitelné ušima.", "steps": ["Tlakové vlny vzduchu slyšitelné ušima.", "Odpověď tedy platí: Tlakové vlny vzduchu slyšitelné ušima."], "text": "Answer: Tlakové vlny vzduchu slyšitelné ušima.\nSteps:\n1. Tlakové vlny vzduchu slyšitelné ušima.\n2. Odpověď tedy platí: Tlakové vlny vzduchu slyšitelné ušima."}
{"id": "phy_0540", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 2000 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "500", "B": "450", "C": "550", "D": "600"}, "answer": "500 atoms remain.", "steps": ["Halve twice: 2000 → 1000 → 500.", "Left: 500.", "Select option A."], "text": "Answer: 500\nSteps:\n1. Halve twice: 2000 → 1000 → 500.\n2. Left: 500.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0541", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why elastic collisions?", "choices": null, "answer": "They conserve kinetic energy too, so balls bounce with speeds solvable exactly.", "steps": ["They conserve kinetic energy too, so balls bounce with speeds solvable exactly.", "So the answer stands: They conserve kinetic energy too, so balls bounce with speeds solvable exactly."], "text": "Answer: They conserve kinetic energy too, so balls bounce with speeds solvable exactly.\nSteps:\n1. They conserve kinetic energy too, so balls bounce with speeds solvable exactly.\n2. So the answer stands: They conserve kinetic energy too, so balls bounce with speeds solvable exactly."}
{"id": "phy_0542", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why light is EM?", "choices": null, "answer": "Maxwell's wave speed matched measured c, revealing light as electromagnetism.", "steps": ["Maxwell's wave speed matched measured c, revealing light as electromagnetism.", "So the answer stands: Maxwell's wave speed matched measured c, revealing light as electromagnetism."], "text": "Answer: Maxwell's wave speed matched measured c, revealing light as electromagnetism.\nSteps:\n1. Maxwell's wave speed matched measured c, revealing light as electromagnetism.\n2. So the answer stands: Maxwell's wave speed matched measured c, revealing light as electromagnetism."}
{"id": "phy_0543", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Kolik tepla ohřeje 2 kg vody o 3 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Teplo: 25116 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 3 K.", "= 25116 J."], "text": "Answer: Teplo: 25116 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 3 K.\n2. = 25116 J."}
{"id": "phy_0544", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what focuses rays?", "choices": {"A": "Mirror", "B": "Prism", "C": "Filter", "D": "Lens"}, "answer": "The answer is Lens.", "steps": ["Glass curves bend.", "So: Lens.", "Select option D."], "text": "Answer: Lens\nSteps:\n1. Glass curves bend.\n2. So: Lens.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0545", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why hearing range?", "choices": null, "answer": "Ears span 20 Hz to 20 kHz, narrowing with age and damage.", "steps": ["Ears span 20 Hz to 20 kHz, narrowing with age and damage.", "So the answer stands: Ears span 20 Hz to 20 kHz, narrowing with age and damage."], "text": "Answer: Ears span 20 Hz to 20 kHz, narrowing with age and damage.\nSteps:\n1. Ears span 20 Hz to 20 kHz, narrowing with age and damage.\n2. So the answer stands: Ears span 20 Hz to 20 kHz, narrowing with age and damage."}
{"id": "phy_0546", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is radioactivity?", "choices": null, "answer": "Unstable nuclei decay randomly with fixed half-lives.", "steps": ["Unstable nuclei decay randomly with fixed half-lives.", "So the answer stands: Unstable nuclei decay randomly with fixed half-lives."], "text": "Answer: Unstable nuclei decay randomly with fixed half-lives.\nSteps:\n1. Unstable nuclei decay randomly with fixed half-lives.\n2. So the answer stands: Unstable nuclei decay randomly with fixed half-lives."}
{"id": "phy_0547", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what pulls springs back?", "choices": {"A": "Hooke's law", "B": "Ohm's law", "C": "Boyle's law", "D": "Moore's law"}, "answer": "The answer is Hooke's law.", "steps": ["Force minus kx.", "So: Hooke's law.", "Select option A."], "text": "Answer: Hooke's law\nSteps:\n1. Force minus kx.\n2. So: Hooke's law.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0548", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 14 s. Compute the energy used.", "choices": null, "answer": "Energy: 1400 J.", "steps": ["E = P×t.", "E = 100 W × 14 s.", "= 1400 J."], "text": "Answer: Energy: 1400 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 14 s.\n3. = 1400 J."}
{"id": "phy_0549", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Kolik tepla ohřeje 1 kg vody o 3 K? (c = 4186 J/(kg·K))", "choices": {"A": "8372 J", "B": "16744 J", "C": "12558 J", "D": "20930 J"}, "answer": "Teplo je 12558 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 3 K.", "Q = 12558 J.", "Vyber možnost C."], "text": "Answer: 12558 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 3 K.\n2. Q = 12558 J.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0550", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why blue sky?", "choices": null, "answer": "Short waves scatter strongest off air, filling heavens with blue.", "steps": ["Short waves scatter strongest off air, filling heavens with blue.", "So the answer stands: Short waves scatter strongest off air, filling heavens with blue."], "text": "Answer: Short waves scatter strongest off air, filling heavens with blue.\nSteps:\n1. Short waves scatter strongest off air, filling heavens with blue.\n2. So the answer stands: Short waves scatter strongest off air, filling heavens with blue."}
{"id": "phy_0551", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is ultrasound?", "choices": null, "answer": "Above-hearing waves image babies and clean parts precisely.", "steps": ["Above-hearing waves image babies and clean parts precisely.", "So the answer stands: Above-hearing waves image babies and clean parts precisely."], "text": "Answer: Above-hearing waves image babies and clean parts precisely.\nSteps:\n1. Above-hearing waves image babies and clean parts precisely.\n2. So the answer stands: Above-hearing waves image babies and clean parts precisely."}
{"id": "phy_0552", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why half-life?", "choices": null, "answer": "Each period halves survivors statistically, dating rocks and relics.", "steps": ["Each period halves survivors statistically, dating rocks and relics.", "So the answer stands: Each period halves survivors statistically, dating rocks and relics."], "text": "Answer: Each period halves survivors statistically, dating rocks and relics.\nSteps:\n1. Each period halves survivors statistically, dating rocks and relics.\n2. So the answer stands: Each period halves survivors statistically, dating rocks and relics."}
{"id": "phy_0553", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 12 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 24 N.", "steps": ["F = m×a.", "F = 12 kg × 2 m/s².", "= 24 N."], "text": "Answer: Net force: 24 N.\nSteps:\n1. F = m×a.\n2. F = 12 kg × 2 m/s².\n3. = 24 N."}
{"id": "phy_0554", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 11 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 363 W.", "steps": ["P = I²×R.", "P = (11 A)² × 3 Ω.", "= 363 W."], "text": "Answer: Power: 363 W.\nSteps:\n1. P = I²×R.\n2. P = (11 A)² × 3 Ω.\n3. = 363 W."}
{"id": "phy_0555", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what hides in bonds?", "choices": {"A": "Loud noise", "B": "Bright light", "C": "Fast wind", "D": "Latent heat"}, "answer": "The answer is Latent heat.", "steps": ["Temp stays flat.", "So: Latent heat.", "Select option D."], "text": "Answer: Latent heat\nSteps:\n1. Temp stays flat.\n2. So: Latent heat.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0556", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what is exactly 299792458?", "choices": {"A": "c in m/s", "B": "g in m/s²", "C": "h in J·s", "D": "e in C"}, "answer": "The answer is c in m/s.", "steps": ["Cosmic limit set.", "So: c in m/s.", "Select option A."], "text": "Answer: c in m/s\nSteps:\n1. Cosmic limit set.\n2. So: c in m/s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0557", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why infrasound?", "choices": null, "answer": "Low rumbles travel far, warning of quakes and storms.", "steps": ["Low rumbles travel far, warning of quakes and storms.", "So the answer stands: Low rumbles travel far, warning of quakes and storms."], "text": "Answer: Low rumbles travel far, warning of quakes and storms.\nSteps:\n1. Low rumbles travel far, warning of quakes and storms.\n2. So the answer stands: Low rumbles travel far, warning of quakes and storms."}
{"id": "phy_0558", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is fission?", "choices": null, "answer": "Heavy nuclei split releasing neutrons and energy, chaining reactors.", "steps": ["Heavy nuclei split releasing neutrons and energy, chaining reactors.", "So the answer stands: Heavy nuclei split releasing neutrons and energy, chaining reactors."], "text": "Answer: Heavy nuclei split releasing neutrons and energy, chaining reactors.\nSteps:\n1. Heavy nuclei split releasing neutrons and energy, chaining reactors.\n2. So the answer stands: Heavy nuclei split releasing neutrons and energy, chaining reactors."}
{"id": "phy_0559", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is torque?", "choices": null, "answer": "Torque is force times lever arm, twisting objects into rotation.", "steps": ["Torque is force times lever arm, twisting objects into rotation.", "So the answer stands: Torque is force times lever arm, twisting objects into rotation."], "text": "Answer: Torque is force times lever arm, twisting objects into rotation.\nSteps:\n1. Torque is force times lever arm, twisting objects into rotation.\n2. So the answer stands: Torque is force times lever arm, twisting objects into rotation."}
{"id": "phy_0560", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 6 A flows through 5 Ω. What is the voltage?", "choices": {"A": "30 V", "B": "25 V", "C": "35 V", "D": "40 V"}, "answer": "Voltage is 30 V.", "steps": ["V = 6 A × 5 Ω.", "V = 30 V.", "Select option A."], "text": "Answer: 30 V\nSteps:\n1. V = 6 A × 5 Ω.\n2. V = 30 V.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0561", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 25 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 298 K.", "steps": ["Add 273.", "25 + 273.", "= 298 K."], "text": "Answer: Temperature: 298 K.\nSteps:\n1. Add 273.\n2. 25 + 273.\n3. = 298 K."}
{"id": "phy_0562", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Obraz vzniká 60 cm od čočky, předmět v 10 cm. Spočítej zvětšení.", "choices": null, "answer": "Zvětšení: 6×.", "steps": ["M = di/do.", "M = 60 cm / 10 cm.", "= 6×."], "text": "Answer: Zvětšení: 6×.\nSteps:\n1. M = di/do.\n2. M = 60 cm / 10 cm.\n3. = 6×."}
{"id": "phy_0563", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 700 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 2100 m/s.", "steps": ["v = f×λ.", "v = 700 Hz × 3 m.", "= 2100 m/s."], "text": "Answer: Speed: 2100 m/s.\nSteps:\n1. v = f×λ.\n2. v = 700 Hz × 3 m.\n3. = 2100 m/s."}
{"id": "phy_0564", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 8800 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 2200.", "steps": ["Halve: 8800 → 4400.", "Halve: 4400 → 2200.", "= 2200."], "text": "Answer: Survivors: 2200.\nSteps:\n1. Halve: 8800 → 4400.\n2. Halve: 4400 → 2200.\n3. = 2200."}
{"id": "phy_0565", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why moment of inertia?", "choices": null, "answer": "It resists angular change like mass resists linear, growing with radius squared.", "steps": ["It resists angular change like mass resists linear, growing with radius squared.", "So the answer stands: It resists angular change like mass resists linear, growing with radius squared."], "text": "Answer: It resists angular change like mass resists linear, growing with radius squared.\nSteps:\n1. It resists angular change like mass resists linear, growing with radius squared.\n2. So the answer stands: It resists angular change like mass resists linear, growing with radius squared."}
{"id": "phy_0566", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 11 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 132 V.", "steps": ["V = I×R.", "V = 11 A × 12 Ω.", "= 132 V."], "text": "Answer: Voltage: 132 V.\nSteps:\n1. V = I×R.\n2. V = 11 A × 12 Ω.\n3. = 132 V."}
{"id": "phy_0567", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 11 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 92092 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 11 K.", "= 92092 J."], "text": "Answer: Heat: 92092 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 11 K.\n2. = 92092 J."}
{"id": "phy_0568", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is a telescope?", "choices": null, "answer": "It gathers faint light with big mirrors, magnifying distant worlds.", "steps": ["It gathers faint light with big mirrors, magnifying distant worlds.", "So the answer stands: It gathers faint light with big mirrors, magnifying distant worlds."], "text": "Answer: It gathers faint light with big mirrors, magnifying distant worlds.\nSteps:\n1. It gathers faint light with big mirrors, magnifying distant worlds.\n2. So the answer stands: It gathers faint light with big mirrors, magnifying distant worlds."}
{"id": "phy_0569", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is the electromagnetic spectrum?", "choices": null, "answer": "Radio to gamma waves differ only in wavelength and energy.", "steps": ["Radio to gamma waves differ only in wavelength and energy.", "So the answer stands: Radio to gamma waves differ only in wavelength and energy."], "text": "Answer: Radio to gamma waves differ only in wavelength and energy.\nSteps:\n1. Radio to gamma waves differ only in wavelength and energy.\n2. So the answer stands: Radio to gamma waves differ only in wavelength and energy."}
{"id": "phy_0570", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why fusion powers stars?", "choices": null, "answer": "Light nuclei merge dropping mass-energy, lighting suns.", "steps": ["Light nuclei merge dropping mass-energy, lighting suns.", "So the answer stands: Light nuclei merge dropping mass-energy, lighting suns."], "text": "Answer: Light nuclei merge dropping mass-energy, lighting suns.\nSteps:\n1. Light nuclei merge dropping mass-energy, lighting suns.\n2. So the answer stands: Light nuclei merge dropping mass-energy, lighting suns."}
{"id": "phy_0571", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 55 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 220 J.", "steps": ["W = F×d.", "W = 55 N × 4 m.", "= 220 J."], "text": "Answer: Work: 220 J.\nSteps:\n1. W = F×d.\n2. W = 55 N × 4 m.\n3. = 220 J."}
{"id": "phy_0572", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "How does polarization cut glare?", "choices": null, "answer": "It filters light's oscillation direction, cutting glare through sunglasses.", "steps": ["It filters light's oscillation direction, cutting glare through sunglasses.", "So the answer stands: It filters light's oscillation direction, cutting glare through sunglasses."], "text": "Answer: It filters light's oscillation direction, cutting glare through sunglasses.\nSteps:\n1. It filters light's oscillation direction, cutting glare through sunglasses.\n2. So the answer stands: It filters light's oscillation direction, cutting glare through sunglasses."}
{"id": "phy_0573", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1500 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 150 W.", "steps": ["P = W/t.", "P = 1500 J / 10 s.", "= 150 W."], "text": "Answer: Power: 150 W.\nSteps:\n1. P = W/t.\n2. P = 1500 J / 10 s.\n3. = 150 W."}
{"id": "phy_0574", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 70 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "6×", "B": "7×", "C": "8×", "D": "9×"}, "answer": "Magnification is 7×.", "steps": ["M = 70 cm / 10 cm.", "M = 7×.", "Select option B."], "text": "Answer: 7×\nSteps:\n1. M = 70 cm / 10 cm.\n2. M = 7×.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0575", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why radio works?", "choices": null, "answer": "Antennas launch metre waves carrying modulated signals far.", "steps": ["Antennas launch metre waves carrying modulated signals far.", "So the answer stands: Antennas launch metre waves carrying modulated signals far."], "text": "Answer: Antennas launch metre waves carrying modulated signals far.\nSteps:\n1. Antennas launch metre waves carrying modulated signals far.\n2. So the answer stands: Antennas launch metre waves carrying modulated signals far."}
{"id": "phy_0576", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 14. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 91.", "steps": ["Pairs: 14×13/2.", "= 182/2.", "= 91."], "text": "Answer: Lines: 91.\nSteps:\n1. Pairs: 14×13/2.\n2. = 182/2.\n3. = 91."}
{"id": "phy_0577", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is angular momentum?", "choices": null, "answer": "Spinning L persists unless torque acts, so skaters speed by pulling arms.", "steps": ["Spinning L persists unless torque acts, so skaters speed by pulling arms.", "So the answer stands: Spinning L persists unless torque acts, so skaters speed by pulling arms."], "text": "Answer: Spinning L persists unless torque acts, so skaters speed by pulling arms.\nSteps:\n1. Spinning L persists unless torque acts, so skaters speed by pulling arms.\n2. So the answer stands: Spinning L persists unless torque acts, so skaters speed by pulling arms."}
{"id": "phy_0578", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 15 s. Compute the energy used.", "choices": null, "answer": "Energy: 1500 J.", "steps": ["E = P×t.", "E = 100 W × 15 s.", "= 1500 J."], "text": "Answer: Energy: 1500 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 15 s.\n3. = 1500 J."}
{"id": "phy_0579", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 26 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 299 K.", "steps": ["Add 273.", "26 + 273.", "= 299 K."], "text": "Answer: Temperature: 299 K.\nSteps:\n1. Add 273.\n2. 26 + 273.\n3. = 299 K."}
{"id": "phy_0580", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 31×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 10.3 s.", "steps": ["t = d/c.", "t = 31×10⁸ / 3×10⁸ s.", "= 10.3 s."], "text": "Answer: Time: 10.3 s.\nSteps:\n1. t = d/c.\n2. t = 31×10⁸ / 3×10⁸ s.\n3. = 10.3 s."}
{"id": "phy_0581", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 12 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 4080 m.", "steps": ["d = v×t.", "d = 340 m/s × 12 s.", "= 4080 m."], "text": "Answer: Distance: 4080 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 12 s.\n3. = 4080 m."}
{"id": "phy_0582", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 13 protons and 14 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 27.", "steps": ["A = Z+N.", "A = 13 + 14.", "= 27."], "text": "Answer: Mass number: 27.\nSteps:\n1. A = Z+N.\n2. A = 13 + 14.\n3. = 27."}
{"id": "phy_0583", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 7 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "18 N", "B": "21 N", "C": "24 N", "D": "27 N"}, "answer": "Net force is 21 N.", "steps": ["F = 7 kg × 3 m/s².", "F = 21 N.", "Select option B."], "text": "Answer: 21 N\nSteps:\n1. F = 7 kg × 3 m/s².\n2. F = 21 N.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0584", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co budí cívky?", "choices": {"A": "měnící se tok", "B": "stálé teplo", "C": "klidný vzduch", "D": "temná místnost"}, "answer": "Odpověď je měnící se tok.", "steps": ["Indukce vládne.", "Tedy: měnící se tok.", "Vyber možnost A."], "text": "Answer: měnící se tok\nSteps:\n1. Indukce vládne.\n2. Tedy: měnící se tok.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0585", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 12 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 100464 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 12 K.", "= 100464 J."], "text": "Answer: Heat: 100464 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 12 K.\n2. = 100464 J."}
{"id": "phy_0586", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Světlo letí 13×10⁸ m. Spočítej dobu letu. (c = 3×10⁸ m/s)", "choices": null, "answer": "Čas: 4,3 s.", "steps": ["t = d/c.", "t = 13×10⁸ / 3×10⁸ s.", "= 4,3 s."], "text": "Answer: Čas: 4,3 s.\nSteps:\n1. t = d/c.\n2. t = 13×10⁸ / 3×10⁸ s.\n3. = 4,3 s."}
{"id": "phy_0587", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 200 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 600 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 200 Hz.", "= 600 Hz."], "text": "Answer: 3rd harmonic: 600 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 200 Hz.\n3. = 600 Hz."}
{"id": "phy_0588", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 9600 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 2400.", "steps": ["Halve: 9600 → 4800.", "Halve: 4800 → 2400.", "= 2400."], "text": "Answer: Survivors: 2400.\nSteps:\n1. Halve: 9600 → 4800.\n2. Halve: 4800 → 2400.\n3. = 2400."}
{"id": "phy_0589", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 14 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 42 kg·m/s.", "steps": ["p = m×v.", "p = 14 kg × 3 m/s.", "= 42 kg·m/s."], "text": "Answer: Momentum: 42 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 14 kg × 3 m/s.\n3. = 42 kg·m/s."}
{"id": "phy_0590", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 4 A teče přes 3 Ω. Spočítej ztrátový výkon.", "choices": null, "answer": "Výkon: 48 W.", "steps": ["P = I²×R.", "P = (4 A)² × 3 Ω.", "= 48 W."], "text": "Answer: Výkon: 48 W.\nSteps:\n1. P = I²×R.\n2. P = (4 A)² × 3 Ω.\n3. = 48 W."}
{"id": "phy_0591", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 24 °C. What is it in kelvin?", "choices": {"A": "297 K", "B": "296 K", "C": "298 K", "D": "299 K"}, "answer": "Temperature is 297 K.", "steps": ["24 °C + 273.", "= 297 K.", "Select option A."], "text": "Answer: 297 K\nSteps:\n1. 24 °C + 273.\n2. = 297 K.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0592", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why big mirrors?", "choices": null, "answer": "Area scales light grasp, so giants see faintest galaxies.", "steps": ["Area scales light grasp, so giants see faintest galaxies.", "So the answer stands: Area scales light grasp, so giants see faintest galaxies."], "text": "Answer: Area scales light grasp, so giants see faintest galaxies.\nSteps:\n1. Area scales light grasp, so giants see faintest galaxies.\n2. So the answer stands: Area scales light grasp, so giants see faintest galaxies."}
{"id": "phy_0593", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 6 Hz. What is its period?", "choices": {"A": "0.14 s", "B": "0.17 s", "C": "0.12 s", "D": "0.2 s"}, "answer": "Period is 0.17 s.", "steps": ["T = 1 / 6 Hz.", "T = 0.17 s.", "Select option B."], "text": "Answer: 0.17 s\nSteps:\n1. T = 1 / 6 Hz.\n2. T = 0.17 s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0594", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 7. How many spectral lines can it emit?", "choices": {"A": "20", "B": "21", "C": "22", "D": "23"}, "answer": "Count: 21.", "steps": ["Pairs: 7×6/2.", "Lines: 21.", "Select option B."], "text": "Answer: 21\nSteps:\n1. Pairs: 7×6/2.\n2. Lines: 21.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0595", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 13 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 26 N.", "steps": ["F = m×a.", "F = 13 kg × 2 m/s².", "= 26 N."], "text": "Answer: Net force: 26 N.\nSteps:\n1. F = m×a.\n2. F = 13 kg × 2 m/s².\n3. = 26 N."}
{"id": "phy_0596", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 7 A. What is its power?", "choices": {"A": "72 W", "B": "84 W", "C": "96 W", "D": "108 W"}, "answer": "Power is 84 W.", "steps": ["P = 12 V × 7 A.", "P = 84 W.", "Select option B."], "text": "Answer: 84 W\nSteps:\n1. P = 12 V × 7 A.\n2. P = 84 W.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0597", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1600 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 160 W.", "steps": ["P = W/t.", "P = 1600 J / 10 s.", "= 160 W."], "text": "Answer: Power: 160 W.\nSteps:\n1. P = W/t.\n2. P = 1600 J / 10 s.\n3. = 160 W."}
{"id": "phy_0598", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 18×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "7 s", "B": "8 s", "C": "6 s", "D": "5 s"}, "answer": "Time is 6 s.", "steps": ["t = 18×10⁸ m / 3×10⁸ m/s.", "t = 6 s.", "Select option C."], "text": "Answer: 6 s\nSteps:\n1. t = 18×10⁸ m / 3×10⁸ m/s.\n2. t = 6 s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0599", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 750 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 2250 m/s.", "steps": ["v = f×λ.", "v = 750 Hz × 3 m.", "= 2250 m/s."], "text": "Answer: Speed: 2250 m/s.\nSteps:\n1. v = f×λ.\n2. v = 750 Hz × 3 m.\n3. = 2250 m/s."}
{"id": "phy_0600", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 15. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 105.", "steps": ["Pairs: 15×14/2.", "= 210/2.", "= 105."], "text": "Answer: Lines: 105.\nSteps:\n1. Pairs: 15×14/2.\n2. = 210/2.\n3. = 105."}
{"id": "phy_0601", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co ohýbá kruhy?", "choices": {"A": "dostředivá síla", "B": "tření", "C": "tíha", "D": "vztlak"}, "answer": "Odpověď je dostředivá síla.", "steps": ["Dovnitř táhne.", "Tedy: dostředivá síla.", "Vyber možnost A."], "text": "Answer: dostředivá síla\nSteps:\n1. Dovnitř táhne.\n2. Tedy: dostředivá síla.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0602", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why grounding?", "choices": null, "answer": "Ground wires sink fault currents safely, protecting people from shocks.", "steps": ["Ground wires sink fault currents safely, protecting people from shocks.", "So the answer stands: Ground wires sink fault currents safely, protecting people from shocks."], "text": "Answer: Ground wires sink fault currents safely, protecting people from shocks.\nSteps:\n1. Ground wires sink fault currents safely, protecting people from shocks.\n2. So the answer stands: Ground wires sink fault currents safely, protecting people from shocks."}
{"id": "phy_0603", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why steam burns?", "choices": null, "answer": "Condensing steam dumps huge latent heat onto skin rapidly.", "steps": ["Condensing steam dumps huge latent heat onto skin rapidly.", "So the answer stands: Condensing steam dumps huge latent heat onto skin rapidly."], "text": "Answer: Condensing steam dumps huge latent heat onto skin rapidly.\nSteps:\n1. Condensing steam dumps huge latent heat onto skin rapidly.\n2. So the answer stands: Condensing steam dumps huge latent heat onto skin rapidly."}
{"id": "phy_0604", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 180 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 120 cm.", "steps": ["d' = d/n.", "d' = 180 cm / 1.5.", "= 120 cm."], "text": "Answer: Apparent depth: 120 cm.\nSteps:\n1. d' = d/n.\n2. d' = 180 cm / 1.5.\n3. = 120 cm."}
{"id": "phy_0605", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What are microwaves?", "choices": null, "answer": "Centimetre waves heat food by shaking water molecules.", "steps": ["Centimetre waves heat food by shaking water molecules.", "So the answer stands: Centimetre waves heat food by shaking water molecules."], "text": "Answer: Centimetre waves heat food by shaking water molecules.\nSteps:\n1. Centimetre waves heat food by shaking water molecules.\n2. So the answer stands: Centimetre waves heat food by shaking water molecules."}
{"id": "phy_0606", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 6 protons and 6 neutrons. What is its mass number?", "choices": {"A": "11", "B": "13", "C": "12", "D": "14"}, "answer": "Mass number is 12.", "steps": ["A = 6 + 6.", "A = 12.", "Select option C."], "text": "Answer: 12\nSteps:\n1. A = 6 + 6.\n2. A = 12.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0607", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why static equilibrium?", "choices": null, "answer": "Zero net force and torque keep structures still, the rule behind bridges.", "steps": ["Zero net force and torque keep structures still, the rule behind bridges.", "So the answer stands: Zero net force and torque keep structures still, the rule behind bridges."], "text": "Answer: Zero net force and torque keep structures still, the rule behind bridges.\nSteps:\n1. Zero net force and torque keep structures still, the rule behind bridges.\n2. So the answer stands: Zero net force and torque keep structures still, the rule behind bridges."}
{"id": "phy_0608", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 12 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 432 W.", "steps": ["P = I²×R.", "P = (12 A)² × 3 Ω.", "= 432 W."], "text": "Answer: Power: 432 W.\nSteps:\n1. P = I²×R.\n2. P = (12 A)² × 3 Ω.\n3. = 432 W."}
{"id": "phy_0609", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 27 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 300 K.", "steps": ["Add 273.", "27 + 273.", "= 300 K."], "text": "Answer: Temperature: 300 K.\nSteps:\n1. Add 273.\n2. 27 + 273.\n3. = 300 K."}
{"id": "phy_0610", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "K čemu čočky?", "choices": null, "answer": "Zakřivené sklo soustřeďuje paprsky do obrazů.", "steps": ["Zakřivené sklo soustřeďuje paprsky do obrazů.", "Odpověď tedy platí: Zakřivené sklo soustřeďuje paprsky do obrazů."], "text": "Answer: Zakřivené sklo soustřeďuje paprsky do obrazů.\nSteps:\n1. Zakřivené sklo soustřeďuje paprsky do obrazů.\n2. Odpověď tedy platí: Zakřivené sklo soustřeďuje paprsky do obrazů."}
{"id": "phy_0611", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 150 Hz. What is its 3rd harmonic?", "choices": {"A": "420 Hz", "B": "480 Hz", "C": "450 Hz", "D": "510 Hz"}, "answer": "3rd harmonic is 450 Hz.", "steps": ["f3 = 3 × 150 Hz.", "f3 = 450 Hz.", "Select option C."], "text": "Answer: 450 Hz\nSteps:\n1. f3 = 3 × 150 Hz.\n2. f3 = 450 Hz.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0612", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 14 protons and 15 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 29.", "steps": ["A = Z+N.", "A = 14 + 15.", "= 29."], "text": "Answer: Mass number: 29.\nSteps:\n1. A = Z+N.\n2. A = 14 + 15.\n3. = 29."}
{"id": "phy_0613", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is Hooke's law?", "choices": null, "answer": "Spring force equals −kx, pulling back proportionally to stretch distance.", "steps": ["Spring force equals −kx, pulling back proportionally to stretch distance.", "So the answer stands: Spring force equals −kx, pulling back proportionally to stretch distance."], "text": "Answer: Spring force equals −kx, pulling back proportionally to stretch distance.\nSteps:\n1. Spring force equals −kx, pulling back proportionally to stretch distance.\n2. So the answer stands: Spring force equals −kx, pulling back proportionally to stretch distance."}
{"id": "phy_0614", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 12 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 144 V.", "steps": ["V = I×R.", "V = 12 A × 12 Ω.", "= 144 V."], "text": "Answer: Voltage: 144 V.\nSteps:\n1. V = I×R.\n2. V = 12 A × 12 Ω.\n3. = 144 V."}
{"id": "phy_0615", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 6 K? (c = 4186 J/(kg·K))", "choices": {"A": "20930 J", "B": "25116 J", "C": "29302 J", "D": "33488 J"}, "answer": "Heat needed is 25116 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 6 K.", "Q = 25116 J.", "Select option B."], "text": "Answer: 25116 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 6 K.\n2. Q = 25116 J.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0616", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is a microscope?", "choices": null, "answer": "Short-focus lenses magnify tiny things hugely in stages.", "steps": ["Short-focus lenses magnify tiny things hugely in stages.", "So the answer stands: Short-focus lenses magnify tiny things hugely in stages."], "text": "Answer: Short-focus lenses magnify tiny things hugely in stages.\nSteps:\n1. Short-focus lenses magnify tiny things hugely in stages.\n2. So the answer stands: Short-focus lenses magnify tiny things hugely in stages."}
{"id": "phy_0617", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what locks into notes?", "choices": {"A": "Running rivers", "B": "Falling rocks", "C": "Flying birds", "D": "Standing waves"}, "answer": "The answer is Standing waves.", "steps": ["Nodes fixed.", "So: Standing waves.", "Select option D."], "text": "Answer: Standing waves\nSteps:\n1. Nodes fixed.\n2. So: Standing waves.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0618", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Proč velký třesk?", "choices": null, "answer": "Prostor se rozpínal z horkého hustého stavu.", "steps": ["Prostor se rozpínal z horkého hustého stavu.", "Odpověď tedy platí: Prostor se rozpínal z horkého hustého stavu."], "text": "Answer: Prostor se rozpínal z horkého hustého stavu.\nSteps:\n1. Prostor se rozpínal z horkého hustého stavu.\n2. Odpověď tedy platí: Prostor se rozpínal z horkého hustého stavu."}
{"id": "phy_0619", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Těleso 3 kg zrychluje 3 m/s². Jaká je výsledná síla?", "choices": {"A": "6 N", "B": "9 N", "C": "12 N", "D": "15 N"}, "answer": "Výsledná síla je 9 N.", "steps": ["F = 3 kg × 3 m/s².", "F = 9 N.", "Vyber možnost B."], "text": "Answer: 9 N\nSteps:\n1. F = 3 kg × 3 m/s².\n2. F = 9 N.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0620", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 16 s. Compute the energy used.", "choices": null, "answer": "Energy: 1600 J.", "steps": ["E = P×t.", "E = 100 W × 16 s.", "= 1600 J."], "text": "Answer: Energy: 1600 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 16 s.\n3. = 1600 J."}
{"id": "phy_0621", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Motor mění 300 J z 1000 J tepla v práci. Jaká je jeho účinnost?", "choices": {"A": "20 %", "B": "40 %", "C": "50 %", "D": "30 %"}, "answer": "Účinnost je 30 %.", "steps": ["300 J / 1000 J.", "= 30 %.", "Vyber možnost D."], "text": "Answer: 30 %\nSteps:\n1. 300 J / 1000 J.\n2. = 30 %.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0622", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 105 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "65 cm", "B": "75 cm", "C": "80 cm", "D": "70 cm"}, "answer": "Apparent depth is 70 cm.", "steps": ["d' = 105 cm / 1.5.", "d' = 70 cm.", "Select option D."], "text": "Answer: 70 cm\nSteps:\n1. d' = 105 cm / 1.5.\n2. d' = 70 cm.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0623", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why X-rays see bones?", "choices": null, "answer": "Short waves pierce flesh but stop at calcium.", "steps": ["Short waves pierce flesh but stop at calcium.", "So the answer stands: Short waves pierce flesh but stop at calcium."], "text": "Answer: Short waves pierce flesh but stop at calcium.\nSteps:\n1. Short waves pierce flesh but stop at calcium.\n2. So the answer stands: Short waves pierce flesh but stop at calcium."}
{"id": "phy_0624", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Vzorek 800 atomů projde 2 poločasy. Kolik atomů zbude?", "choices": {"A": "150", "B": "200", "C": "250", "D": "300"}, "answer": "Zbude 200 atomů.", "steps": ["Půlit dvakrát: 800 → 400 → 200.", "Zbývá: 200.", "Vyber možnost B."], "text": "Answer: 200\nSteps:\n1. Půlit dvakrát: 800 → 400 → 200.\n2. Zbývá: 200.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0625", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 6 kg zrychluje 2 m/s². Spočítej výslednou sílu.", "choices": null, "answer": "Výsledná síla: 12 N.", "steps": ["F = m×a.", "F = 6 kg × 2 m/s².", "= 12 N."], "text": "Answer: Výsledná síla: 12 N.\nSteps:\n1. F = m×a.\n2. F = 6 kg × 2 m/s².\n3. = 12 N."}
{"id": "phy_0626", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 30 s. How much charge passes?", "choices": {"A": "100 C", "B": "140 C", "C": "120 C", "D": "160 C"}, "answer": "Charge is 120 C.", "steps": ["Q = 4 A × 30 s.", "Q = 120 C.", "Select option C."], "text": "Answer: 120 C\nSteps:\n1. Q = 4 A × 30 s.\n2. Q = 120 C.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0627", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 600 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "50%", "B": "70%", "C": "60%", "D": "80%"}, "answer": "Efficiency is 60%.", "steps": ["600 J / 1000 J.", "= 60%.", "Select option C."], "text": "Answer: 60%\nSteps:\n1. 600 J / 1000 J.\n2. = 60%.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0628", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 130 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 13×.", "steps": ["M = di/do.", "M = 130 cm / 10 cm.", "= 13×."], "text": "Answer: Magnification: 13×.\nSteps:\n1. M = di/do.\n2. M = 130 cm / 10 cm.\n3. = 13×."}
{"id": "phy_0629", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 13 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 4420 m.", "steps": ["d = v×t.", "d = 340 m/s × 13 s.", "= 4420 m."], "text": "Answer: Distance: 4420 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 13 s.\n3. = 4420 m."}
{"id": "phy_0630", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is the Standard Model?", "choices": null, "answer": "Quarks, leptons, and bosons explain all known particles and forces.", "steps": ["Quarks, leptons, and bosons explain all known particles and forces.", "So the answer stands: Quarks, leptons, and bosons explain all known particles and forces."], "text": "Answer: Quarks, leptons, and bosons explain all known particles and forces.\nSteps:\n1. Quarks, leptons, and bosons explain all known particles and forces.\n2. So the answer stands: Quarks, leptons, and bosons explain all known particles and forces."}
{"id": "phy_0631", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Auto ujede 110 m za 10 s. Jaká je jeho rychlost?", "choices": {"A": "10 m/s", "B": "12 m/s", "C": "11 m/s", "D": "13 m/s"}, "answer": "Rychlost je 11 m/s.", "steps": ["v = 110 m / 10 s.", "v = 11 m/s.", "Vyber možnost C."], "text": "Answer: 11 m/s\nSteps:\n1. v = 110 m / 10 s.\n2. v = 11 m/s.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0632", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what does motion create?", "choices": {"A": "Gravity well", "B": "Sound wave", "C": "Heat haze", "D": "Magnetic field"}, "answer": "The answer is Magnetic field.", "steps": ["Currents loop fields.", "So: Magnetic field.", "Select option D."], "text": "Answer: Magnetic field\nSteps:\n1. Currents loop fields.\n2. So: Magnetic field.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0633", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is thermal equilibrium?", "choices": null, "answer": "Equal temperatures stop net heat flow, defining temperature itself.", "steps": ["Equal temperatures stop net heat flow, defining temperature itself.", "So the answer stands: Equal temperatures stop net heat flow, defining temperature itself."], "text": "Answer: Equal temperatures stop net heat flow, defining temperature itself.\nSteps:\n1. Equal temperatures stop net heat flow, defining temperature itself.\n2. So the answer stands: Equal temperatures stop net heat flow, defining temperature itself."}
{"id": "phy_0634", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why oil immersion?", "choices": null, "answer": "Oil raises numerical aperture, resolving finer detail sharply.", "steps": ["Oil raises numerical aperture, resolving finer detail sharply.", "So the answer stands: Oil raises numerical aperture, resolving finer detail sharply."], "text": "Answer: Oil raises numerical aperture, resolving finer detail sharply.\nSteps:\n1. Oil raises numerical aperture, resolving finer detail sharply.\n2. So the answer stands: Oil raises numerical aperture, resolving finer detail sharply."}
{"id": "phy_0635", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is wave interference?", "choices": null, "answer": "Overlapping waves sum by phase, building holograms and noise control.", "steps": ["Overlapping waves sum by phase, building holograms and noise control.", "So the answer stands: Overlapping waves sum by phase, building holograms and noise control."], "text": "Answer: Overlapping waves sum by phase, building holograms and noise control.\nSteps:\n1. Overlapping waves sum by phase, building holograms and noise control.\n2. So the answer stands: Overlapping waves sum by phase, building holograms and noise control."}
{"id": "phy_0636", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what halves statistically?", "choices": {"A": "Full moon", "B": "High tide", "C": "Leap year", "D": "Half-life"}, "answer": "The answer is Half-life.", "steps": ["Rocks dated.", "So: Half-life.", "Select option D."], "text": "Answer: Half-life\nSteps:\n1. Rocks dated.\n2. So: Half-life.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0637", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why simple harmonic motion?", "choices": null, "answer": "Restoring force linear in displacement makes sinusoidal oscillation with fixed period.", "steps": ["Restoring force linear in displacement makes sinusoidal oscillation with fixed period.", "So the answer stands: Restoring force linear in displacement makes sinusoidal oscillation with fixed period."], "text": "Answer: Restoring force linear in displacement makes sinusoidal oscillation with fixed period.\nSteps:\n1. Restoring force linear in displacement makes sinusoidal oscillation with fixed period.\n2. So the answer stands: Restoring force linear in displacement makes sinusoidal oscillation with fixed period."}
{"id": "phy_0638", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 13 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 507 W.", "steps": ["P = I²×R.", "P = (13 A)² × 3 Ω.", "= 507 W."], "text": "Answer: Power: 507 W.\nSteps:\n1. P = I²×R.\n2. P = (13 A)² × 3 Ω.\n3. = 507 W."}
{"id": "phy_0639", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what hands energy along?", "choices": {"A": "Singing", "B": "Dancing", "C": "Sleeping", "D": "Conduction"}, "answer": "The answer is Conduction.", "steps": ["Collisions pass heat.", "So: Conduction.", "Select option D."], "text": "Answer: Conduction\nSteps:\n1. Collisions pass heat.\n2. So: Conduction.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0640", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Proč ohnisková vzdálenost?", "choices": null, "answer": "Značí setkání rovnoběžných paprsků.", "steps": ["Značí setkání rovnoběžných paprsků.", "Odpověď tedy platí: Značí setkání rovnoběžných paprsků."], "text": "Answer: Značí setkání rovnoběžných paprsků.\nSteps:\n1. Značí setkání rovnoběžných paprsků.\n2. Odpověď tedy platí: Značí setkání rovnoběžných paprsků."}
{"id": "phy_0641", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why noise cancelling?", "choices": null, "answer": "Anti-phase sound erases rumble, silencing cabins and headphones.", "steps": ["Anti-phase sound erases rumble, silencing cabins and headphones.", "So the answer stands: Anti-phase sound erases rumble, silencing cabins and headphones."], "text": "Answer: Anti-phase sound erases rumble, silencing cabins and headphones.\nSteps:\n1. Anti-phase sound erases rumble, silencing cabins and headphones.\n2. So the answer stands: Anti-phase sound erases rumble, silencing cabins and headphones."}
{"id": "phy_0642", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 10400 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 2600.", "steps": ["Halve: 10400 → 5200.", "Halve: 5200 → 2600.", "= 2600."], "text": "Answer: Survivors: 2600.\nSteps:\n1. Halve: 10400 → 5200.\n2. Halve: 5200 → 2600.\n3. = 2600."}
{"id": "phy_0643", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 60 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 240 J.", "steps": ["W = F×d.", "W = 60 N × 4 m.", "= 240 J."], "text": "Answer: Work: 240 J.\nSteps:\n1. W = F×d.\n2. W = 60 N × 4 m.\n3. = 240 J."}
{"id": "phy_0644", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "Choose: what melts to save?", "choices": {"A": "Fuse", "B": "Bulb", "C": "Wire", "D": "Plug"}, "answer": "The answer is Fuse.", "steps": ["Excess sacrificed.", "So: Fuse.", "Select option A."], "text": "Answer: Fuse\nSteps:\n1. Excess sacrificed.\n2. So: Fuse.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0645", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Choose: what peaks by temperature?", "choices": {"A": "Blackbody glow", "B": "Neon sign", "C": "Candle flame", "D": "Laser dot"}, "answer": "The answer is Blackbody glow.", "steps": ["Quanta founded.", "So: Blackbody glow.", "Select option A."], "text": "Answer: Blackbody glow\nSteps:\n1. Quanta founded.\n2. So: Blackbody glow.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0646", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is resolution?", "choices": null, "answer": "Diffraction limits smallest separable spots to wavelength over aperture.", "steps": ["Diffraction limits smallest separable spots to wavelength over aperture.", "So the answer stands: Diffraction limits smallest separable spots to wavelength over aperture."], "text": "Answer: Diffraction limits smallest separable spots to wavelength over aperture.\nSteps:\n1. Diffraction limits smallest separable spots to wavelength over aperture.\n2. So the answer stands: Diffraction limits smallest separable spots to wavelength over aperture."}
{"id": "phy_0647", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Hrom je slyšet 4 s po blesku. Jak daleko je bouře? (v = 340 m/s)", "choices": null, "answer": "Vzdálenost: 1360 m.", "steps": ["d = v×t.", "d = 340 m/s × 4 s.", "= 1360 m."], "text": "Answer: Vzdálenost: 1360 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 4 s.\n3. = 1360 m."}
{"id": "phy_0648", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Atom je vybuzen do hladiny n = 4. Kolik spektrálních čar může vyzářit?", "choices": {"A": "5", "B": "7", "C": "6", "D": "8"}, "answer": "Počet: 6.", "steps": ["Dvojice: 4×3/2.", "Čar: 6.", "Vyber možnost C."], "text": "Answer: 6\nSteps:\n1. Dvojice: 4×3/2.\n2. Čar: 6.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0649", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 150 m in 10 s. What is its speed?", "choices": {"A": "14 m/s", "B": "16 m/s", "C": "15 m/s", "D": "17 m/s"}, "answer": "Speed is 15 m/s.", "steps": ["v = 150 m / 10 s.", "v = 15 m/s.", "Select option C."], "text": "Answer: 15 m/s\nSteps:\n1. v = 150 m / 10 s.\n2. v = 15 m/s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0650", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is a fuse?", "choices": null, "answer": "Fuses melt at excess current, sacrificing themselves to save circuits.", "steps": ["Fuses melt at excess current, sacrificing themselves to save circuits.", "So the answer stands: Fuses melt at excess current, sacrificing themselves to save circuits."], "text": "Answer: Fuses melt at excess current, sacrificing themselves to save circuits.\nSteps:\n1. Fuses melt at excess current, sacrificing themselves to save circuits.\n2. So the answer stands: Fuses melt at excess current, sacrificing themselves to save circuits."}
{"id": "phy_0651", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 13 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 108836 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 13 K.", "= 108836 J."], "text": "Answer: Heat: 108836 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 13 K.\n2. = 108836 J."}
{"id": "phy_0652", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 34×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 11.3 s.", "steps": ["t = d/c.", "t = 34×10⁸ / 3×10⁸ s.", "= 11.3 s."], "text": "Answer: Time: 11.3 s.\nSteps:\n1. t = d/c.\n2. t = 34×10⁸ / 3×10⁸ s.\n3. = 11.3 s."}
{"id": "phy_0653", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Proč Dopplerův jev?", "choices": null, "answer": "Pohyb posouvá slyšenou frekvenci.", "steps": ["Pohyb posouvá slyšenou frekvenci.", "Odpověď tedy platí: Pohyb posouvá slyšenou frekvenci."], "text": "Answer: Pohyb posouvá slyšenou frekvenci.\nSteps:\n1. Pohyb posouvá slyšenou frekvenci.\n2. Odpověď tedy platí: Pohyb posouvá slyšenou frekvenci."}
{"id": "phy_0654", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Atom je vybuzen do hladiny n = 6. Spočítej čáry, jež může vyzářit.", "choices": null, "answer": "Čar: 15.", "steps": ["Dvojice: 6×5/2.", "= 30/2.", "= 15."], "text": "Answer: Čar: 15.\nSteps:\n1. Dvojice: 6×5/2.\n2. = 30/2.\n3. = 15."}
{"id": "phy_0655", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 9 m/s. What is its kinetic energy?", "choices": {"A": "72 J", "B": "90 J", "C": "99 J", "D": "81 J"}, "answer": "Kinetic energy is 81 J.", "steps": ["KE = ½×2 kg×(9 m/s)².", "KE = 81 J.", "Select option D."], "text": "Answer: 81 J\nSteps:\n1. KE = ½×2 kg×(9 m/s)².\n2. KE = 81 J.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0656", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why three-phase?", "choices": null, "answer": "Three offset phases deliver steady power, running industry smoothly.", "steps": ["Three offset phases deliver steady power, running industry smoothly.", "So the answer stands: Three offset phases deliver steady power, running industry smoothly."], "text": "Answer: Three offset phases deliver steady power, running industry smoothly.\nSteps:\n1. Three offset phases deliver steady power, running industry smoothly.\n2. So the answer stands: Three offset phases deliver steady power, running industry smoothly."}
{"id": "phy_0657", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 25 °C. What is it in kelvin?", "choices": {"A": "297 K", "B": "298 K", "C": "299 K", "D": "300 K"}, "answer": "Temperature is 298 K.", "steps": ["25 °C + 273.", "= 298 K.", "Select option B."], "text": "Answer: 298 K\nSteps:\n1. 25 °C + 273.\n2. = 298 K.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0658", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Předmět leží 90 cm hluboko ve skle (n = 1,5). Spočítej zdánlivou hloubku.", "choices": null, "answer": "Zdánlivá hloubka: 60 cm.", "steps": ["d' = d/n.", "d' = 90 cm / 1,5.", "= 60 cm."], "text": "Answer: Zdánlivá hloubka: 60 cm.\nSteps:\n1. d' = d/n.\n2. d' = 90 cm / 1,5.\n3. = 60 cm."}
{"id": "phy_0659", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 210 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 630 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 210 Hz.", "= 630 Hz."], "text": "Answer: 3rd harmonic: 630 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 210 Hz.\n3. = 630 Hz."}
{"id": "phy_0660", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Jádro má 5 protonů a 6 neutronů. Spočítej jeho nukleonové číslo.", "choices": null, "answer": "Nukleonové číslo: 11.", "steps": ["A = Z+N.", "A = 5 + 6.", "= 11."], "text": "Answer: Nukleonové číslo: 11.\nSteps:\n1. A = Z+N.\n2. A = 5 + 6.\n3. = 11."}
{"id": "phy_0661", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Síla 25 N tlačí na dráze 4 m. Spočítej vykonanou práci.", "choices": null, "answer": "Práce: 100 J.", "steps": ["W = F×d.", "W = 25 N × 4 m.", "= 100 J."], "text": "Answer: Práce: 100 J.\nSteps:\n1. W = F×d.\n2. W = 25 N × 4 m.\n3. = 100 J."}
{"id": "phy_0662", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 13 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 156 V.", "steps": ["V = I×R.", "V = 13 A × 12 Ω.", "= 156 V."], "text": "Answer: Voltage: 156 V.\nSteps:\n1. V = I×R.\n2. V = 13 A × 12 Ω.\n3. = 156 V."}
{"id": "phy_0663", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Motor vykoná 700 J práce za 10 s. Spočítej jeho výkon.", "choices": null, "answer": "Výkon: 70 W.", "steps": ["P = W/t.", "P = 700 J / 10 s.", "= 70 W."], "text": "Answer: Výkon: 70 W.\nSteps:\n1. P = W/t.\n2. P = 700 J / 10 s.\n3. = 70 W."}
{"id": "phy_0664", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Co je zvětšení?", "choices": null, "answer": "Velikost obrazu ku předmětu.", "steps": ["Velikost obrazu ku předmětu.", "Odpověď tedy platí: Velikost obrazu ku předmětu."], "text": "Answer: Velikost obrazu ku předmětu.\nSteps:\n1. Velikost obrazu ku předmětu.\n2. Odpověď tedy platí: Velikost obrazu ku předmětu."}
{"id": "phy_0665", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "Choose: what proves photons?", "choices": {"A": "Photoelectric", "B": "Photosynthesis", "C": "Photography", "D": "Photocopy"}, "answer": "The answer is Photoelectric.", "steps": ["Threshold rules.", "So: Photoelectric.", "Select option A."], "text": "Answer: Photoelectric\nSteps:\n1. Threshold rules.\n2. So: Photoelectric.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0666", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 16. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 120.", "steps": ["Pairs: 16×15/2.", "= 240/2.", "= 120."], "text": "Answer: Lines: 120.\nSteps:\n1. Pairs: 16×15/2.\n2. = 240/2.\n3. = 120."}
{"id": "phy_0667", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 8 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "21 N", "B": "27 N", "C": "24 N", "D": "30 N"}, "answer": "Net force is 24 N.", "steps": ["F = 8 kg × 3 m/s².", "F = 24 N.", "Select option C."], "text": "Answer: 24 N\nSteps:\n1. F = 8 kg × 3 m/s².\n2. F = 24 N.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0668", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Co je proud?", "choices": null, "answer": "Proud je tok náboje za sekundu v ampérech.", "steps": ["Proud je tok náboje za sekundu v ampérech.", "Odpověď tedy platí: Proud je tok náboje za sekundu v ampérech."], "text": "Answer: Proud je tok náboje za sekundu v ampérech.\nSteps:\n1. Proud je tok náboje za sekundu v ampérech.\n2. Odpověď tedy platí: Proud je tok náboje za sekundu v ampérech."}
{"id": "phy_0669", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1700 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 170 W.", "steps": ["P = W/t.", "P = 1700 J / 10 s.", "= 170 W."], "text": "Answer: Power: 170 W.\nSteps:\n1. P = W/t.\n2. P = 1700 J / 10 s.\n3. = 170 W."}
{"id": "phy_0670", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 80 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "7×", "B": "9×", "C": "8×", "D": "10×"}, "answer": "Magnification is 8×.", "steps": ["M = 80 cm / 10 cm.", "M = 8×.", "Select option C."], "text": "Answer: 8×\nSteps:\n1. M = 80 cm / 10 cm.\n2. M = 8×.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0671", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 800 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 2400 m/s.", "steps": ["v = f×λ.", "v = 800 Hz × 3 m.", "= 2400 m/s."], "text": "Answer: Speed: 2400 m/s.\nSteps:\n1. v = f×λ.\n2. v = 800 Hz × 3 m.\n3. = 2400 m/s."}
{"id": "phy_0672", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 15 protons and 16 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 31.", "steps": ["A = Z+N.", "A = 15 + 16.", "= 31."], "text": "Answer: Mass number: 31.\nSteps:\n1. A = Z+N.\n2. A = 15 + 16.\n3. = 31."}
{"id": "phy_0673", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 15 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 45 kg·m/s.", "steps": ["p = m×v.", "p = 15 kg × 3 m/s.", "= 45 kg·m/s."], "text": "Answer: Momentum: 45 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 15 kg × 3 m/s.\n3. = 45 kg·m/s."}
{"id": "phy_0674", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is a semiconductor?", "choices": null, "answer": "Doped silicon conducts controllably, the basis of all electronics.", "steps": ["Doped silicon conducts controllably, the basis of all electronics.", "So the answer stands: Doped silicon conducts controllably, the basis of all electronics."], "text": "Answer: Doped silicon conducts controllably, the basis of all electronics.\nSteps:\n1. Doped silicon conducts controllably, the basis of all electronics.\n2. So the answer stands: Doped silicon conducts controllably, the basis of all electronics."}
{"id": "phy_0675", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 7 K? (c = 4186 J/(kg·K))", "choices": {"A": "25116 J", "B": "33488 J", "C": "29302 J", "D": "37674 J"}, "answer": "Heat needed is 29302 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 7 K.", "Q = 29302 J.", "Select option C."], "text": "Answer: 29302 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 7 K.\n2. Q = 29302 J.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0676", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Proč zobrazovací rovnice?", "choices": null, "answer": "1/f rovná se 1/a + 1/a', určuje polohu obrazu.", "steps": ["1/f rovná se 1/a + 1/a', určuje polohu obrazu.", "Odpověď tedy platí: 1/f rovná se 1/a + 1/a', určuje polohu obrazu."], "text": "Answer: 1/f rovná se 1/a + 1/a', určuje polohu obrazu.\nSteps:\n1. 1/f rovná se 1/a + 1/a', určuje polohu obrazu.\n2. Odpověď tedy platí: 1/f rovná se 1/a + 1/a', určuje polohu obrazu."}
{"id": "phy_0677", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 350 Hz and λ = 2 m. What is its speed?", "choices": {"A": "650 m/s", "B": "700 m/s", "C": "750 m/s", "D": "800 m/s"}, "answer": "Speed is 700 m/s.", "steps": ["v = 350 Hz × 2 m.", "v = 700 m/s.", "Select option B."], "text": "Answer: 700 m/s\nSteps:\n1. v = 350 Hz × 2 m.\n2. v = 700 m/s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0678", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why the Higgs?", "choices": null, "answer": "Its field drags particles giving mass, found in 2012.", "steps": ["Its field drags particles giving mass, found in 2012.", "So the answer stands: Its field drags particles giving mass, found in 2012."], "text": "Answer: Its field drags particles giving mass, found in 2012.\nSteps:\n1. Its field drags particles giving mass, found in 2012.\n2. So the answer stands: Its field drags particles giving mass, found in 2012."}
{"id": "phy_0679", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 8 kg se pohybuje 3 m/s. Spočítej jeho hybnost.", "choices": null, "answer": "Hybnost: 24 kg·m/s.", "steps": ["p = m×v.", "p = 8 kg × 3 m/s.", "= 24 kg·m/s."], "text": "Answer: Hybnost: 24 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 8 kg × 3 m/s.\n3. = 24 kg·m/s."}
{"id": "phy_0680", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 17 s. Compute the energy used.", "choices": null, "answer": "Energy: 1700 J.", "steps": ["E = P×t.", "E = 100 W × 17 s.", "= 1700 J."], "text": "Answer: Energy: 1700 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 17 s.\n3. = 1700 J."}
{"id": "phy_0681", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co začíná v nulovém pohybu?", "choices": {"A": "Kelvinova stupnice", "B": "Celsiova stupnice", "C": "Beaufortova stupnice", "D": "Richterova stupnice"}, "answer": "Odpověď je Kelvinova stupnice.", "steps": ["Absolutní nula základem.", "Tedy: Kelvinova stupnice.", "Vyber možnost A."], "text": "Answer: Kelvinova stupnice\nSteps:\n1. Absolutní nula základem.\n2. Tedy: Kelvinova stupnice.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0682", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 195 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 130 cm.", "steps": ["d' = d/n.", "d' = 195 cm / 1.5.", "= 130 cm."], "text": "Answer: Apparent depth: 130 cm.\nSteps:\n1. d' = d/n.\n2. d' = 195 cm / 1.5.\n3. = 130 cm."}
{"id": "phy_0683", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 7 Hz. What is its period?", "choices": {"A": "0.12 s", "B": "0.11 s", "C": "0.14 s", "D": "0.17 s"}, "answer": "Period is 0.14 s.", "steps": ["T = 1 / 7 Hz.", "T = 0.14 s.", "Select option C."], "text": "Answer: 0.14 s\nSteps:\n1. T = 1 / 7 Hz.\n2. T = 0.14 s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0684", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is antimatter?", "choices": null, "answer": "Mirror particles annihilate on contact, fuelling sci-fi and PET scans.", "steps": ["Mirror particles annihilate on contact, fuelling sci-fi and PET scans.", "So the answer stands: Mirror particles annihilate on contact, fuelling sci-fi and PET scans."], "text": "Answer: Mirror particles annihilate on contact, fuelling sci-fi and PET scans.\nSteps:\n1. Mirror particles annihilate on contact, fuelling sci-fi and PET scans.\n2. So the answer stands: Mirror particles annihilate on contact, fuelling sci-fi and PET scans."}
{"id": "phy_0685", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 14 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 28 N.", "steps": ["F = m×a.", "F = 14 kg × 2 m/s².", "= 28 N."], "text": "Answer: Net force: 28 N.\nSteps:\n1. F = m×a.\n2. F = 14 kg × 2 m/s².\n3. = 28 N."}
{"id": "phy_0686", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why diodes?", "choices": null, "answer": "One-way valves pass current forward only, rectifying AC into DC.", "steps": ["One-way valves pass current forward only, rectifying AC into DC.", "So the answer stands: One-way valves pass current forward only, rectifying AC into DC."], "text": "Answer: One-way valves pass current forward only, rectifying AC into DC.\nSteps:\n1. One-way valves pass current forward only, rectifying AC into DC.\n2. So the answer stands: One-way valves pass current forward only, rectifying AC into DC."}
{"id": "phy_0687", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why zeroth law?", "choices": null, "answer": "If A matches C and B matches C, A matches B, grounding thermometers.", "steps": ["If A matches C and B matches C, A matches B, grounding thermometers.", "So the answer stands: If A matches C and B matches C, A matches B, grounding thermometers."], "text": "Answer: If A matches C and B matches C, A matches B, grounding thermometers.\nSteps:\n1. If A matches C and B matches C, A matches B, grounding thermometers.\n2. So the answer stands: If A matches C and B matches C, A matches B, grounding thermometers."}
{"id": "phy_0688", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 140 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 14×.", "steps": ["M = di/do.", "M = 140 cm / 10 cm.", "= 14×."], "text": "Answer: Magnification: 14×.\nSteps:\n1. M = di/do.\n2. M = 140 cm / 10 cm.\n3. = 14×."}
{"id": "phy_0689", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 14 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 4760 m.", "steps": ["d = v×t.", "d = 340 m/s × 14 s.", "= 4760 m."], "text": "Answer: Distance: 4760 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 14 s.\n3. = 4760 m."}
{"id": "phy_0690", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Vzorek 3200 atomů projde 2 poločasy. Spočítej přeživší.", "choices": null, "answer": "Přeživší: 800.", "steps": ["Půl: 3200 → 1600.", "Půl: 1600 → 800.", "= 800."], "text": "Answer: Přeživší: 800.\nSteps:\n1. Půl: 3200 → 1600.\n2. Půl: 1600 → 800.\n3. = 800."}
{"id": "phy_0691", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 65 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 260 J.", "steps": ["W = F×d.", "W = 65 N × 4 m.", "= 260 J."], "text": "Answer: Work: 260 J.\nSteps:\n1. W = F×d.\n2. W = 65 N × 4 m.\n3. = 260 J."}
{"id": "phy_0692", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 14 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 588 W.", "steps": ["P = I²×R.", "P = (14 A)² × 3 Ω.", "= 588 W."], "text": "Answer: Power: 588 W.\nSteps:\n1. P = I²×R.\n2. P = (14 A)² × 3 Ω.\n3. = 588 W."}
{"id": "phy_0693", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Co je druhý zákon?", "choices": null, "answer": "Entropie izolovaných soustav nikdy neklesá.", "steps": ["Entropie izolovaných soustav nikdy neklesá.", "Odpověď tedy platí: Entropie izolovaných soustav nikdy neklesá."], "text": "Answer: Entropie izolovaných soustav nikdy neklesá.\nSteps:\n1. Entropie izolovaných soustav nikdy neklesá.\n2. Odpověď tedy platí: Entropie izolovaných soustav nikdy neklesá."}
{"id": "phy_0694", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 37×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 12.3 s.", "steps": ["t = d/c.", "t = 37×10⁸ / 3×10⁸ s.", "= 12.3 s."], "text": "Answer: Time: 12.3 s.\nSteps:\n1. t = d/c.\n2. t = 37×10⁸ / 3×10⁸ s.\n3. = 12.3 s."}
{"id": "phy_0695", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 220 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 660 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 220 Hz.", "= 660 Hz."], "text": "Answer: 3rd harmonic: 660 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 220 Hz.\n3. = 660 Hz."}
{"id": "phy_0696", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Jádro má 3 protonů a 3 neutronů. Jaké je jeho nukleonové číslo?", "choices": {"A": "5", "B": "7", "C": "8", "D": "6"}, "answer": "Nukleonové číslo je 6.", "steps": ["A = 3 + 3.", "A = 6.", "Vyber možnost D."], "text": "Answer: 6\nSteps:\n1. A = 3 + 3.\n2. A = 6.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0697", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Proč kinetická energie?", "choices": null, "answer": "Pohybující se hmotnost nese ½mv².", "steps": ["Pohybující se hmotnost nese ½mv².", "Odpověď tedy platí: Pohybující se hmotnost nese ½mv²."], "text": "Answer: Pohybující se hmotnost nese ½mv².\nSteps:\n1. Pohybující se hmotnost nese ½mv².\n2. Odpověď tedy platí: Pohybující se hmotnost nese ½mv²."}
{"id": "phy_0698", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 7 A flows through 5 Ω. What is the voltage?", "choices": {"A": "30 V", "B": "35 V", "C": "40 V", "D": "45 V"}, "answer": "Voltage is 35 V.", "steps": ["V = 7 A × 5 Ω.", "V = 35 V.", "Select option B."], "text": "Answer: 35 V\nSteps:\n1. V = 7 A × 5 Ω.\n2. V = 35 V.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0699", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is heat capacity?", "choices": null, "answer": "It is joules per degree for a whole object, scaling with mass.", "steps": ["It is joules per degree for a whole object, scaling with mass.", "So the answer stands: It is joules per degree for a whole object, scaling with mass."], "text": "Answer: It is joules per degree for a whole object, scaling with mass.\nSteps:\n1. It is joules per degree for a whole object, scaling with mass.\n2. So the answer stands: It is joules per degree for a whole object, scaling with mass."}
{"id": "phy_0700", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 210 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 140 cm.", "steps": ["d' = d/n.", "d' = 210 cm / 1.5.", "= 140 cm."], "text": "Answer: Apparent depth: 140 cm.\nSteps:\n1. d' = d/n.\n2. d' = 210 cm / 1.5.\n3. = 140 cm."}
{"id": "phy_0701", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "How does diffraction turn corners?", "choices": null, "answer": "Waves spread past edges, letting sound turn corners.", "steps": ["Waves spread past edges, letting sound turn corners.", "So the answer stands: Waves spread past edges, letting sound turn corners."], "text": "Answer: Waves spread past edges, letting sound turn corners.\nSteps:\n1. Waves spread past edges, letting sound turn corners.\n2. So the answer stands: Waves spread past edges, letting sound turn corners."}
{"id": "phy_0702", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why PET scans?", "choices": null, "answer": "Annihilation photons pinpoint tracers inside bodies precisely.", "steps": ["Annihilation photons pinpoint tracers inside bodies precisely.", "So the answer stands: Annihilation photons pinpoint tracers inside bodies precisely."], "text": "Answer: Annihilation photons pinpoint tracers inside bodies precisely.\nSteps:\n1. Annihilation photons pinpoint tracers inside bodies precisely.\n2. So the answer stands: Annihilation photons pinpoint tracers inside bodies precisely."}
{"id": "phy_0703", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 16 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 48 kg·m/s.", "steps": ["p = m×v.", "p = 16 kg × 3 m/s.", "= 48 kg·m/s."], "text": "Answer: Momentum: 48 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 16 kg × 3 m/s.\n3. = 48 kg·m/s."}
{"id": "phy_0704", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is a transistor?", "choices": null, "answer": "Tiny gates switch big currents, amplifying signals into computers.", "steps": ["Tiny gates switch big currents, amplifying signals into computers.", "So the answer stands: Tiny gates switch big currents, amplifying signals into computers."], "text": "Answer: Tiny gates switch big currents, amplifying signals into computers.\nSteps:\n1. Tiny gates switch big currents, amplifying signals into computers.\n2. So the answer stands: Tiny gates switch big currents, amplifying signals into computers."}
{"id": "phy_0705", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 28 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 301 K.", "steps": ["Add 273.", "28 + 273.", "= 301 K."], "text": "Answer: Temperature: 301 K.\nSteps:\n1. Add 273.\n2. 28 + 273.\n3. = 301 K."}
{"id": "phy_0706", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Předmět leží 45 cm hluboko ve skle (n = 1,5). Jaká je zdánlivá hloubka?", "choices": {"A": "25 cm", "B": "35 cm", "C": "40 cm", "D": "30 cm"}, "answer": "Zdánlivá hloubka je 30 cm.", "steps": ["d' = 45 cm / 1,5.", "d' = 30 cm.", "Vyber možnost D."], "text": "Answer: 30 cm\nSteps:\n1. d' = 45 cm / 1,5.\n2. d' = 30 cm.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0707", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why waveguides?", "choices": null, "answer": "Pipes channel microwaves efficiently to antennas and ovens.", "steps": ["Pipes channel microwaves efficiently to antennas and ovens.", "So the answer stands: Pipes channel microwaves efficiently to antennas and ovens."], "text": "Answer: Pipes channel microwaves efficiently to antennas and ovens.\nSteps:\n1. Pipes channel microwaves efficiently to antennas and ovens.\n2. So the answer stands: Pipes channel microwaves efficiently to antennas and ovens."}
{"id": "phy_0708", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co tiká pomaleji?", "choices": {"A": "pohybující se hodiny", "B": "rozbité hodinky", "C": "zastavené minutky", "D": "ztracené telefony"}, "answer": "Odpověď je pohybující se hodiny.", "steps": ["Miony potvrzují.", "Tedy: pohybující se hodiny.", "Vyber možnost A."], "text": "Answer: pohybující se hodiny\nSteps:\n1. Miony potvrzují.\n2. Tedy: pohybující se hodiny.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0709", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Co je hybnost?", "choices": null, "answer": "Hybnost mv přetrvává srážkami.", "steps": ["Hybnost mv přetrvává srážkami.", "Odpověď tedy platí: Hybnost mv přetrvává srážkami."], "text": "Answer: Hybnost mv přetrvává srážkami.\nSteps:\n1. Hybnost mv přetrvává srážkami.\n2. Odpověď tedy platí: Hybnost mv přetrvává srážkami."}
{"id": "phy_0710", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 14 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 168 V.", "steps": ["V = I×R.", "V = 14 A × 12 Ω.", "= 168 V."], "text": "Answer: Voltage: 168 V.\nSteps:\n1. V = I×R.\n2. V = 14 A × 12 Ω.\n3. = 168 V."}
{"id": "phy_0711", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 700 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "60%", "B": "80%", "C": "90%", "D": "70%"}, "answer": "Efficiency is 70%.", "steps": ["700 J / 1000 J.", "= 70%.", "Select option D."], "text": "Answer: 70%\nSteps:\n1. 700 J / 1000 J.\n2. = 70%.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0712", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 21×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "8 s", "B": "9 s", "C": "6 s", "D": "7 s"}, "answer": "Time is 7 s.", "steps": ["t = 21×10⁸ m / 3×10⁸ m/s.", "t = 7 s.", "Select option D."], "text": "Answer: 7 s\nSteps:\n1. t = 21×10⁸ m / 3×10⁸ m/s.\n2. t = 7 s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0713", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co váže rychlost a cykly?", "choices": {"A": "v rovná se fλ", "B": "E rovná se mc", "C": "F rovná se ma", "D": "pV rovná se nRT"}, "answer": "Odpověď je v rovná se fλ.", "steps": ["Hlavní vztah držen.", "Tedy: v rovná se fλ.", "Vyber možnost A."], "text": "Answer: v rovná se fλ\nSteps:\n1. Hlavní vztah držen.\n2. Tedy: v rovná se fλ.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0714", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 11200 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 2800.", "steps": ["Halve: 11200 → 5600.", "Halve: 5600 → 2800.", "= 2800."], "text": "Answer: Survivors: 2800.\nSteps:\n1. Halve: 11200 → 5600.\n2. Halve: 5600 → 2800.\n3. = 2800."}
{"id": "phy_0715", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 15 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 30 N.", "steps": ["F = m×a.", "F = 15 kg × 2 m/s².", "= 30 N."], "text": "Answer: Net force: 30 N.\nSteps:\n1. F = m×a.\n2. F = 15 kg × 2 m/s².\n3. = 30 N."}
{"id": "phy_0716", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 18 s. Compute the energy used.", "choices": null, "answer": "Energy: 1800 J.", "steps": ["E = P×t.", "E = 100 W × 18 s.", "= 1800 J."], "text": "Answer: Energy: 1800 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 18 s.\n3. = 1800 J."}
{"id": "phy_0717", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why calorimetry?", "choices": null, "answer": "Insulated mixing reveals unknown heats by balancing lost and gained energy.", "steps": ["Insulated mixing reveals unknown heats by balancing lost and gained energy.", "So the answer stands: Insulated mixing reveals unknown heats by balancing lost and gained energy."], "text": "Answer: Insulated mixing reveals unknown heats by balancing lost and gained energy.\nSteps:\n1. Insulated mixing reveals unknown heats by balancing lost and gained energy.\n2. So the answer stands: Insulated mixing reveals unknown heats by balancing lost and gained energy."}
{"id": "phy_0718", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 150 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 15×.", "steps": ["M = di/do.", "M = 150 cm / 10 cm.", "= 15×."], "text": "Answer: Magnification: 15×.\nSteps:\n1. M = di/do.\n2. M = 150 cm / 10 cm.\n3. = 15×."}
{"id": "phy_0719", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is a tsunami?", "choices": null, "answer": "Long ocean waves race at jet speed with huge energy.", "steps": ["Long ocean waves race at jet speed with huge energy.", "So the answer stands: Long ocean waves race at jet speed with huge energy."], "text": "Answer: Long ocean waves race at jet speed with huge energy.\nSteps:\n1. Long ocean waves race at jet speed with huge energy.\n2. So the answer stands: Long ocean waves race at jet speed with huge energy."}
{"id": "phy_0720", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is superconductivity?", "choices": null, "answer": "Paired electrons flow losslessly below critical cold.", "steps": ["Paired electrons flow losslessly below critical cold.", "So the answer stands: Paired electrons flow losslessly below critical cold."], "text": "Answer: Paired electrons flow losslessly below critical cold.\nSteps:\n1. Paired electrons flow losslessly below critical cold.\n2. So the answer stands: Paired electrons flow losslessly below critical cold."}
{"id": "phy_0721", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 160 m in 10 s. What is its speed?", "choices": {"A": "15 m/s", "B": "17 m/s", "C": "18 m/s", "D": "16 m/s"}, "answer": "Speed is 16 m/s.", "steps": ["v = 160 m / 10 s.", "v = 16 m/s.", "Select option D."], "text": "Answer: 16 m/s\nSteps:\n1. v = 160 m / 10 s.\n2. v = 16 m/s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0722", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 8 A. What is its power?", "choices": {"A": "84 W", "B": "108 W", "C": "96 W", "D": "120 W"}, "answer": "Power is 96 W.", "steps": ["P = 12 V × 8 A.", "P = 96 W.", "Select option C."], "text": "Answer: 96 W\nSteps:\n1. P = 12 V × 8 A.\n2. P = 96 W.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0723", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 14 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 117208 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 14 K.", "= 117208 J."], "text": "Answer: Heat: 117208 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 14 K.\n2. = 117208 J."}
{"id": "phy_0724", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why Rayleigh criterion?", "choices": null, "answer": "It marks when two spots just separate, timing optics precisely.", "steps": ["It marks when two spots just separate, timing optics precisely.", "So the answer stands: It marks when two spots just separate, timing optics precisely."], "text": "Answer: It marks when two spots just separate, timing optics precisely.\nSteps:\n1. It marks when two spots just separate, timing optics precisely.\n2. So the answer stands: It marks when two spots just separate, timing optics precisely."}
{"id": "phy_0725", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 850 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 2550 m/s.", "steps": ["v = f×λ.", "v = 850 Hz × 3 m.", "= 2550 m/s."], "text": "Answer: Speed: 2550 m/s.\nSteps:\n1. v = f×λ.\n2. v = 850 Hz × 3 m.\n3. = 2550 m/s."}
{"id": "phy_0726", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why quantum computers?", "choices": null, "answer": "Superposed qubits explore many paths at once for select tasks.", "steps": ["Superposed qubits explore many paths at once for select tasks.", "So the answer stands: Superposed qubits explore many paths at once for select tasks."], "text": "Answer: Superposed qubits explore many paths at once for select tasks.\nSteps:\n1. Superposed qubits explore many paths at once for select tasks.\n2. So the answer stands: Superposed qubits explore many paths at once for select tasks."}
{"id": "phy_0727", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is a pendulum's period?", "choices": null, "answer": "Small swings take 2π√(L/g), depending on length, not on mass or amplitude.", "steps": ["Small swings take 2π√(L/g), depending on length, not on mass or amplitude.", "So the answer stands: Small swings take 2π√(L/g), depending on length, not on mass or amplitude."], "text": "Answer: Small swings take 2π√(L/g), depending on length, not on mass or amplitude.\nSteps:\n1. Small swings take 2π√(L/g), depending on length, not on mass or amplitude.\n2. So the answer stands: Small swings take 2π√(L/g), depending on length, not on mass or amplitude."}
{"id": "phy_0728", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 35 s. How much charge passes?", "choices": {"A": "120 C", "B": "160 C", "C": "180 C", "D": "140 C"}, "answer": "Charge is 140 C.", "steps": ["Q = 4 A × 35 s.", "Q = 140 C.", "Select option D."], "text": "Answer: 140 C\nSteps:\n1. Q = 4 A × 35 s.\n2. Q = 140 C.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0729", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 26 °C. What is it in kelvin?", "choices": {"A": "298 K", "B": "300 K", "C": "299 K", "D": "301 K"}, "answer": "Temperature is 299 K.", "steps": ["26 °C + 273.", "= 299 K.", "Select option C."], "text": "Answer: 299 K\nSteps:\n1. 26 °C + 273.\n2. = 299 K.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0730", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 40×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 13.3 s.", "steps": ["t = d/c.", "t = 40×10⁸ / 3×10⁸ s.", "= 13.3 s."], "text": "Answer: Time: 13.3 s.\nSteps:\n1. t = d/c.\n2. t = 40×10⁸ / 3×10⁸ s.\n3. = 13.3 s."}
{"id": "phy_0731", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co logaritmuje hlasitost?", "choices": {"A": "metr", "B": "decibel", "C": "sekunda", "D": "gram"}, "answer": "Odpověď je decibel.", "steps": ["Výkon poměřen.", "Tedy: decibel.", "Vyber možnost B."], "text": "Answer: decibel\nSteps:\n1. Výkon poměřen.\n2. Tedy: decibel.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0732", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 17. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 136.", "steps": ["Pairs: 17×16/2.", "= 272/2.", "= 136."], "text": "Answer: Lines: 136.\nSteps:\n1. Pairs: 17×16/2.\n2. = 272/2.\n3. = 136."}
{"id": "phy_0733", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why resonance?", "choices": null, "answer": "Driving at natural frequency pumps amplitude hugely, shattering glasses and bridges.", "steps": ["Driving at natural frequency pumps amplitude hugely, shattering glasses and bridges.", "So the answer stands: Driving at natural frequency pumps amplitude hugely, shattering glasses and bridges."], "text": "Answer: Driving at natural frequency pumps amplitude hugely, shattering glasses and bridges.\nSteps:\n1. Driving at natural frequency pumps amplitude hugely, shattering glasses and bridges.\n2. So the answer stands: Driving at natural frequency pumps amplitude hugely, shattering glasses and bridges."}
{"id": "phy_0734", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Proč odpor?", "choices": null, "answer": "Srážky uvnitř vodičů brání driftu.", "steps": ["Srážky uvnitř vodičů brání driftu.", "Odpověď tedy platí: Srážky uvnitř vodičů brání driftu."], "text": "Answer: Srážky uvnitř vodičů brání driftu.\nSteps:\n1. Srážky uvnitř vodičů brání driftu.\n2. Odpověď tedy platí: Srážky uvnitř vodičů brání driftu."}
{"id": "phy_0735", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is thermal conductivity?", "choices": null, "answer": "It rates heat flow per gradient, high in copper, low in wool.", "steps": ["It rates heat flow per gradient, high in copper, low in wool.", "So the answer stands: It rates heat flow per gradient, high in copper, low in wool."], "text": "Answer: It rates heat flow per gradient, high in copper, low in wool.\nSteps:\n1. It rates heat flow per gradient, high in copper, low in wool.\n2. So the answer stands: It rates heat flow per gradient, high in copper, low in wool."}
{"id": "phy_0736", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 120 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "80 cm", "B": "75 cm", "C": "85 cm", "D": "90 cm"}, "answer": "Apparent depth is 80 cm.", "steps": ["d' = 120 cm / 1.5.", "d' = 80 cm.", "Select option A."], "text": "Answer: 80 cm\nSteps:\n1. d' = 120 cm / 1.5.\n2. d' = 80 cm.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0737", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 15 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 5100 m.", "steps": ["d = v×t.", "d = 340 m/s × 15 s.", "= 5100 m."], "text": "Answer: Distance: 5100 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 15 s.\n3. = 5100 m."}
{"id": "phy_0738", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "Choose: what shares no state?", "choices": {"A": "Pauli fermions", "B": "Chatty neighbours", "C": "Noisy crowds", "D": "Busy bees"}, "answer": "The answer is Pauli fermions.", "steps": ["Table built.", "So: Pauli fermions.", "Select option A."], "text": "Answer: Pauli fermions\nSteps:\n1. Table built.\n2. So: Pauli fermions.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0739", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 10 m/s. What is its kinetic energy?", "choices": {"A": "100 J", "B": "90 J", "C": "110 J", "D": "120 J"}, "answer": "Kinetic energy is 100 J.", "steps": ["KE = ½×2 kg×(10 m/s)².", "KE = 100 J.", "Select option A."], "text": "Answer: 100 J\nSteps:\n1. KE = ½×2 kg×(10 m/s)².\n2. KE = 100 J.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0740", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why superconductors?", "choices": null, "answer": "Zero resistance below critical temperature carries current forever losslessly.", "steps": ["Zero resistance below critical temperature carries current forever losslessly.", "So the answer stands: Zero resistance below critical temperature carries current forever losslessly."], "text": "Answer: Zero resistance below critical temperature carries current forever losslessly.\nSteps:\n1. Zero resistance below critical temperature carries current forever losslessly.\n2. So the answer stands: Zero resistance below critical temperature carries current forever losslessly."}
{"id": "phy_0741", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Teplota je 18 °C. Převeď ji na kelviny.", "choices": null, "answer": "Teplota: 291 K.", "steps": ["Přičti 273.", "18 + 273.", "= 291 K."], "text": "Answer: Teplota: 291 K.\nSteps:\n1. Přičti 273.\n2. 18 + 273.\n3. = 291 K."}
{"id": "phy_0742", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is a laser?", "choices": null, "answer": "Stimulated emission makes coherent intense beams, cutting and reading precisely.", "steps": ["Stimulated emission makes coherent intense beams, cutting and reading precisely.", "So the answer stands: Stimulated emission makes coherent intense beams, cutting and reading precisely."], "text": "Answer: Stimulated emission makes coherent intense beams, cutting and reading precisely.\nSteps:\n1. Stimulated emission makes coherent intense beams, cutting and reading precisely.\n2. So the answer stands: Stimulated emission makes coherent intense beams, cutting and reading precisely."}
{"id": "phy_0743", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 160 Hz. What is its 3rd harmonic?", "choices": {"A": "450 Hz", "B": "510 Hz", "C": "540 Hz", "D": "480 Hz"}, "answer": "3rd harmonic is 480 Hz.", "steps": ["f3 = 3 × 160 Hz.", "f3 = 480 Hz.", "Select option D."], "text": "Answer: 480 Hz\nSteps:\n1. f3 = 3 × 160 Hz.\n2. f3 = 480 Hz.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0744", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 2400 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "550", "B": "600", "C": "650", "D": "700"}, "answer": "600 atoms remain.", "steps": ["Halve twice: 2400 → 1200 → 600.", "Left: 600.", "Select option B."], "text": "Answer: 600\nSteps:\n1. Halve twice: 2400 → 1200 → 600.\n2. Left: 600.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0745", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 9 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "24 N", "B": "30 N", "C": "33 N", "D": "27 N"}, "answer": "Net force is 27 N.", "steps": ["F = 9 kg × 3 m/s².", "F = 27 N.", "Select option D."], "text": "Answer: 27 N\nSteps:\n1. F = 9 kg × 3 m/s².\n2. F = 27 N.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0746", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 8 A flows through 5 Ω. What is the voltage?", "choices": {"A": "35 V", "B": "45 V", "C": "40 V", "D": "50 V"}, "answer": "Voltage is 40 V.", "steps": ["V = 8 A × 5 Ω.", "V = 40 V.", "Select option C."], "text": "Answer: 40 V\nSteps:\n1. V = 8 A × 5 Ω.\n2. V = 40 V.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0747", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co stropuje všechny stroje?", "choices": {"A": "rychlostní limit", "B": "Carnotova mez", "C": "váhový limit", "D": "věkový limit"}, "answer": "Odpověď je Carnotova mez.", "steps": ["Poměr teplot váže.", "Tedy: Carnotova mez.", "Vyber možnost B."], "text": "Answer: Carnotova mez\nSteps:\n1. Poměr teplot váže.\n2. Tedy: Carnotova mez.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0748", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 225 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 150 cm.", "steps": ["d' = d/n.", "d' = 225 cm / 1.5.", "= 150 cm."], "text": "Answer: Apparent depth: 150 cm.\nSteps:\n1. d' = d/n.\n2. d' = 225 cm / 1.5.\n3. = 150 cm."}
{"id": "phy_0749", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 400 Hz and λ = 2 m. What is its speed?", "choices": {"A": "750 m/s", "B": "850 m/s", "C": "800 m/s", "D": "900 m/s"}, "answer": "Speed is 800 m/s.", "steps": ["v = 400 Hz × 2 m.", "v = 800 m/s.", "Select option C."], "text": "Answer: 800 m/s\nSteps:\n1. v = 400 Hz × 2 m.\n2. v = 800 m/s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0750", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Co je kvantová mechanika?", "choices": null, "answer": "Mikrosvět se řídí vlnovými pravidly.", "steps": ["Mikrosvět se řídí vlnovými pravidly.", "Odpověď tedy platí: Mikrosvět se řídí vlnovými pravidly."], "text": "Answer: Mikrosvět se řídí vlnovými pravidly.\nSteps:\n1. Mikrosvět se řídí vlnovými pravidly.\n2. Odpověď tedy platí: Mikrosvět se řídí vlnovými pravidly."}
{"id": "phy_0751", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 170 m in 10 s. What is its speed?", "choices": {"A": "17 m/s", "B": "16 m/s", "C": "18 m/s", "D": "19 m/s"}, "answer": "Speed is 17 m/s.", "steps": ["v = 170 m / 10 s.", "v = 17 m/s.", "Select option A."], "text": "Answer: 17 m/s\nSteps:\n1. v = 170 m / 10 s.\n2. v = 17 m/s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0752", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is Hall effect?", "choices": null, "answer": "Sideways voltage reveals charge sign and density in conductors.", "steps": ["Sideways voltage reveals charge sign and density in conductors.", "So the answer stands: Sideways voltage reveals charge sign and density in conductors."], "text": "Answer: Sideways voltage reveals charge sign and density in conductors.\nSteps:\n1. Sideways voltage reveals charge sign and density in conductors.\n2. So the answer stands: Sideways voltage reveals charge sign and density in conductors."}
{"id": "phy_0753", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why insulation?", "choices": null, "answer": "Trapped air slows conduction and convection, keeping houses warm cheaply.", "steps": ["Trapped air slows conduction and convection, keeping houses warm cheaply.", "So the answer stands: Trapped air slows conduction and convection, keeping houses warm cheaply."], "text": "Answer: Trapped air slows conduction and convection, keeping houses warm cheaply.\nSteps:\n1. Trapped air slows conduction and convection, keeping houses warm cheaply.\n2. So the answer stands: Trapped air slows conduction and convection, keeping houses warm cheaply."}
{"id": "phy_0754", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 160 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 16×.", "steps": ["M = di/do.", "M = 160 cm / 10 cm.", "= 16×."], "text": "Answer: Magnification: 16×.\nSteps:\n1. M = di/do.\n2. M = 160 cm / 10 cm.\n3. = 16×."}
{"id": "phy_0755", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why tides differ?", "choices": null, "answer": "Tides are slow gravitational sloshes, not wind-driven waves.", "steps": ["Tides are slow gravitational sloshes, not wind-driven waves.", "So the answer stands: Tides are slow gravitational sloshes, not wind-driven waves."], "text": "Answer: Tides are slow gravitational sloshes, not wind-driven waves.\nSteps:\n1. Tides are slow gravitational sloshes, not wind-driven waves.\n2. So the answer stands: Tides are slow gravitational sloshes, not wind-driven waves."}
{"id": "phy_0756", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Atom je vybuzen do hladiny n = 7. Spočítej čáry, jež může vyzářit.", "choices": null, "answer": "Čar: 21.", "steps": ["Dvojice: 7×6/2.", "= 42/2.", "= 21."], "text": "Answer: Čar: 21.\nSteps:\n1. Dvojice: 7×6/2.\n2. = 42/2.\n3. = 21."}
{"id": "phy_0757", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 70 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 280 J.", "steps": ["W = F×d.", "W = 70 N × 4 m.", "= 280 J."], "text": "Answer: Work: 280 J.\nSteps:\n1. W = F×d.\n2. W = 70 N × 4 m.\n3. = 280 J."}
{"id": "phy_0758", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 15 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 675 W.", "steps": ["P = I²×R.", "P = (15 A)² × 3 Ω.", "= 675 W."], "text": "Answer: Power: 675 W.\nSteps:\n1. P = I²×R.\n2. P = (15 A)² × 3 Ω.\n3. = 675 W."}
{"id": "phy_0759", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1800 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 180 W.", "steps": ["P = W/t.", "P = 1800 J / 10 s.", "= 180 W."], "text": "Answer: Power: 180 W.\nSteps:\n1. P = W/t.\n2. P = 1800 J / 10 s.\n3. = 180 W."}
{"id": "phy_0760", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 90 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "8×", "B": "10×", "C": "11×", "D": "9×"}, "answer": "Magnification is 9×.", "steps": ["M = 90 cm / 10 cm.", "M = 9×.", "Select option D."], "text": "Answer: 9×\nSteps:\n1. M = 90 cm / 10 cm.\n2. M = 9×.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0761", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 230 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 690 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 230 Hz.", "= 690 Hz."], "text": "Answer: 3rd harmonic: 690 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 230 Hz.\n3. = 690 Hz."}
{"id": "phy_0762", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 16 protons and 17 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 33.", "steps": ["A = Z+N.", "A = 16 + 17.", "= 33."], "text": "Answer: Mass number: 33.\nSteps:\n1. A = Z+N.\n2. A = 16 + 17.\n3. = 33."}
{"id": "phy_0763", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 17 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 51 kg·m/s.", "steps": ["p = m×v.", "p = 17 kg × 3 m/s.", "= 51 kg·m/s."], "text": "Answer: Momentum: 51 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 17 kg × 3 m/s.\n3. = 51 kg·m/s."}
{"id": "phy_0764", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Co je elektrický výkon?", "choices": null, "answer": "Výkon UI ve wattech.", "steps": ["Výkon UI ve wattech.", "Odpověď tedy platí: Výkon UI ve wattech."], "text": "Answer: Výkon UI ve wattech.\nSteps:\n1. Výkon UI ve wattech.\n2. Odpověď tedy platí: Výkon UI ve wattech."}
{"id": "phy_0765", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is blackbody radiation?", "choices": null, "answer": "Hot objects glow with spectra set by temperature alone, founding quantum theory.", "steps": ["Hot objects glow with spectra set by temperature alone, founding quantum theory.", "So the answer stands: Hot objects glow with spectra set by temperature alone, founding quantum theory."], "text": "Answer: Hot objects glow with spectra set by temperature alone, founding quantum theory.\nSteps:\n1. Hot objects glow with spectra set by temperature alone, founding quantum theory.\n2. So the answer stands: Hot objects glow with spectra set by temperature alone, founding quantum theory."}
{"id": "phy_0766", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 24×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "8 s", "B": "9 s", "C": "10 s", "D": "7 s"}, "answer": "Time is 8 s.", "steps": ["t = 24×10⁸ m / 3×10⁸ m/s.", "t = 8 s.", "Select option A."], "text": "Answer: 8 s\nSteps:\n1. t = 24×10⁸ m / 3×10⁸ m/s.\n2. t = 8 s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0767", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 8 Hz. What is its period?", "choices": {"A": "0.11 s", "B": "0.1 s", "C": "0.14 s", "D": "0.12 s"}, "answer": "Period is 0.12 s.", "steps": ["T = 1 / 8 Hz.", "T = 0.12 s.", "Select option D."], "text": "Answer: 0.12 s\nSteps:\n1. T = 1 / 8 Hz.\n2. T = 0.12 s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0768", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 12000 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 3000.", "steps": ["Halve: 12000 → 6000.", "Halve: 6000 → 3000.", "= 3000."], "text": "Answer: Survivors: 3000.\nSteps:\n1. Halve: 12000 → 6000.\n2. Halve: 6000 → 3000.\n3. = 3000."}
{"id": "phy_0769", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is escape velocity?", "choices": null, "answer": "It is the speed to leave a planet forever, 11.2 km/s from Earth.", "steps": ["It is the speed to leave a planet forever, 11.2 km/s from Earth.", "So the answer stands: It is the speed to leave a planet forever, 11.2 km/s from Earth."], "text": "Answer: It is the speed to leave a planet forever, 11.2 km/s from Earth.\nSteps:\n1. It is the speed to leave a planet forever, 11.2 km/s from Earth.\n2. So the answer stands: It is the speed to leave a planet forever, 11.2 km/s from Earth."}
{"id": "phy_0770", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 4 A teče přes 12 Ω. Spočítej napětí.", "choices": null, "answer": "Napětí: 48 V.", "steps": ["U = I×R.", "U = 4 A × 12 Ω.", "= 48 V."], "text": "Answer: Napětí: 48 V.\nSteps:\n1. U = I×R.\n2. U = 4 A × 12 Ω.\n3. = 48 V."}
{"id": "phy_0771", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why Stefan-Boltzmann?", "choices": null, "answer": "Radiated power scales with T⁴, so small heating boosts glow hugely.", "steps": ["Radiated power scales with T⁴, so small heating boosts glow hugely.", "So the answer stands: Radiated power scales with T⁴, so small heating boosts glow hugely."], "text": "Answer: Radiated power scales with T⁴, so small heating boosts glow hugely.\nSteps:\n1. Radiated power scales with T⁴, so small heating boosts glow hugely.\n2. So the answer stands: Radiated power scales with T⁴, so small heating boosts glow hugely."}
{"id": "phy_0772", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 43×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 14.3 s.", "steps": ["t = d/c.", "t = 43×10⁸ / 3×10⁸ s.", "= 14.3 s."], "text": "Answer: Time: 14.3 s.\nSteps:\n1. t = d/c.\n2. t = 43×10⁸ / 3×10⁸ s.\n3. = 14.3 s."}
{"id": "phy_0773", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is a shock wave?", "choices": null, "answer": "Abrupt pressure jumps from blasts outrun sound itself.", "steps": ["Abrupt pressure jumps from blasts outrun sound itself.", "So the answer stands: Abrupt pressure jumps from blasts outrun sound itself."], "text": "Answer: Abrupt pressure jumps from blasts outrun sound itself.\nSteps:\n1. Abrupt pressure jumps from blasts outrun sound itself.\n2. So the answer stands: Abrupt pressure jumps from blasts outrun sound itself."}
{"id": "phy_0774", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 18. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 153.", "steps": ["Pairs: 18×17/2.", "= 306/2.", "= 153."], "text": "Answer: Lines: 153.\nSteps:\n1. Pairs: 18×17/2.\n2. = 306/2.\n3. = 153."}
{"id": "phy_0775", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 16 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 32 N.", "steps": ["F = m×a.", "F = 16 kg × 2 m/s².", "= 32 N."], "text": "Answer: Net force: 32 N.\nSteps:\n1. F = m×a.\n2. F = 16 kg × 2 m/s².\n3. = 32 N."}
{"id": "phy_0776", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 9 A. What is its power?", "choices": {"A": "96 W", "B": "120 W", "C": "132 W", "D": "108 W"}, "answer": "Power is 108 W.", "steps": ["P = 12 V × 9 A.", "P = 108 W.", "Select option D."], "text": "Answer: 108 W\nSteps:\n1. P = 12 V × 9 A.\n2. P = 108 W.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0777", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 29 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 302 K.", "steps": ["Add 273.", "29 + 273.", "= 302 K."], "text": "Answer: Temperature: 302 K.\nSteps:\n1. Add 273.\n2. 29 + 273.\n3. = 302 K."}
{"id": "phy_0778", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why coherence matters?", "choices": null, "answer": "Locked phases let beams interfere and focus tightly over distance.", "steps": ["Locked phases let beams interfere and focus tightly over distance.", "So the answer stands: Locked phases let beams interfere and focus tightly over distance."], "text": "Answer: Locked phases let beams interfere and focus tightly over distance.\nSteps:\n1. Locked phases let beams interfere and focus tightly over distance.\n2. So the answer stands: Locked phases let beams interfere and focus tightly over distance."}
{"id": "phy_0779", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 900 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 2700 m/s.", "steps": ["v = f×λ.", "v = 900 Hz × 3 m.", "= 2700 m/s."], "text": "Answer: Speed: 2700 m/s.\nSteps:\n1. v = f×λ.\n2. v = 900 Hz × 3 m.\n3. = 2700 m/s."}
{"id": "phy_0780", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is decoherence?", "choices": null, "answer": "Environment leaks quantumness away, turning blends classical.", "steps": ["Environment leaks quantumness away, turning blends classical.", "So the answer stands: Environment leaks quantumness away, turning blends classical."], "text": "Answer: Environment leaks quantumness away, turning blends classical.\nSteps:\n1. Environment leaks quantumness away, turning blends classical.\n2. So the answer stands: Environment leaks quantumness away, turning blends classical."}
{"id": "phy_0781", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 75 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 300 J.", "steps": ["W = F×d.", "W = 75 N × 4 m.", "= 300 J."], "text": "Answer: Work: 300 J.\nSteps:\n1. W = F×d.\n2. W = 75 N × 4 m.\n3. = 300 J."}
{"id": "phy_0782", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 15 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 180 V.", "steps": ["V = I×R.", "V = 15 A × 12 Ω.", "= 180 V."], "text": "Answer: Voltage: 180 V.\nSteps:\n1. V = I×R.\n2. V = 15 A × 12 Ω.\n3. = 180 V."}
{"id": "phy_0783", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 8 K? (c = 4186 J/(kg·K))", "choices": {"A": "29302 J", "B": "37674 J", "C": "41860 J", "D": "33488 J"}, "answer": "Heat needed is 33488 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 8 K.", "Q = 33488 J.", "Select option D."], "text": "Answer: 33488 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 8 K.\n2. Q = 33488 J.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0784", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is holography?", "choices": null, "answer": "Recorded interference rebuilds 3D light fields viewable around.", "steps": ["Recorded interference rebuilds 3D light fields viewable around.", "So the answer stands: Recorded interference rebuilds 3D light fields viewable around."], "text": "Answer: Recorded interference rebuilds 3D light fields viewable around.\nSteps:\n1. Recorded interference rebuilds 3D light fields viewable around.\n2. So the answer stands: Recorded interference rebuilds 3D light fields viewable around."}
{"id": "phy_0785", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 170 Hz. What is its 3rd harmonic?", "choices": {"A": "510 Hz", "B": "480 Hz", "C": "540 Hz", "D": "570 Hz"}, "answer": "3rd harmonic is 510 Hz.", "steps": ["f3 = 3 × 170 Hz.", "f3 = 510 Hz.", "Select option A."], "text": "Answer: 510 Hz\nSteps:\n1. f3 = 3 × 170 Hz.\n2. f3 = 510 Hz.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0786", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why uncertainty?", "choices": null, "answer": "Conjugate pairs share spread limits set by Planck's constant.", "steps": ["Conjugate pairs share spread limits set by Planck's constant.", "So the answer stands: Conjugate pairs share spread limits set by Planck's constant."], "text": "Answer: Conjugate pairs share spread limits set by Planck's constant.\nSteps:\n1. Conjugate pairs share spread limits set by Planck's constant.\n2. So the answer stands: Conjugate pairs share spread limits set by Planck's constant."}
{"id": "phy_0787", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 11 m/s. What is its kinetic energy?", "choices": {"A": "110 J", "B": "121 J", "C": "132 J", "D": "143 J"}, "answer": "Kinetic energy is 121 J.", "steps": ["KE = ½×2 kg×(11 m/s)².", "KE = 121 J.", "Select option B."], "text": "Answer: 121 J\nSteps:\n1. KE = ½×2 kg×(11 m/s)².\n2. KE = 121 J.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0788", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Proud 3 A teče přes 5 Ω. Jaké je napětí?", "choices": {"A": "10 V", "B": "15 V", "C": "20 V", "D": "25 V"}, "answer": "Napětí je 15 V.", "steps": ["U = 3 A × 5 Ω.", "U = 15 V.", "Vyber možnost B."], "text": "Answer: 15 V\nSteps:\n1. U = 3 A × 5 Ω.\n2. U = 15 V.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0789", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 800 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "80%", "B": "70%", "C": "90%", "D": "100%"}, "answer": "Efficiency is 80%.", "steps": ["800 J / 1000 J.", "= 80%.", "Select option A."], "text": "Answer: 80%\nSteps:\n1. 800 J / 1000 J.\n2. = 80%.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0790", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Co je rozklad světla?", "choices": null, "answer": "Sklo ohýbá barvy různě.", "steps": ["Sklo ohýbá barvy různě.", "Odpověď tedy platí: Sklo ohýbá barvy různě."], "text": "Answer: Sklo ohýbá barvy různě.\nSteps:\n1. Sklo ohýbá barvy různě.\n2. Odpověď tedy platí: Sklo ohýbá barvy různě."}
{"id": "phy_0791", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 16 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 5440 m.", "steps": ["d = v×t.", "d = 340 m/s × 16 s.", "= 5440 m."], "text": "Answer: Distance: 5440 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 16 s.\n3. = 5440 m."}
{"id": "phy_0792", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is spin?", "choices": null, "answer": "Intrinsic angular momentum with two outcomes, not real rotation.", "steps": ["Intrinsic angular momentum with two outcomes, not real rotation.", "So the answer stands: Intrinsic angular momentum with two outcomes, not real rotation."], "text": "Answer: Intrinsic angular momentum with two outcomes, not real rotation.\nSteps:\n1. Intrinsic angular momentum with two outcomes, not real rotation.\n2. So the answer stands: Intrinsic angular momentum with two outcomes, not real rotation."}
{"id": "phy_0793", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why orbits ellipse?", "choices": null, "answer": "Inverse-square gravity binds planets to ellipses, with speed varying by distance.", "steps": ["Inverse-square gravity binds planets to ellipses, with speed varying by distance.", "So the answer stands: Inverse-square gravity binds planets to ellipses, with speed varying by distance."], "text": "Answer: Inverse-square gravity binds planets to ellipses, with speed varying by distance.\nSteps:\n1. Inverse-square gravity binds planets to ellipses, with speed varying by distance.\n2. So the answer stands: Inverse-square gravity binds planets to ellipses, with speed varying by distance."}
{"id": "phy_0794", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Žárovka běží na 12 V a bere 4 A. Jaký je její příkon?", "choices": {"A": "36 W", "B": "60 W", "C": "48 W", "D": "72 W"}, "answer": "Příkon je 48 W.", "steps": ["P = 12 V × 4 A.", "P = 48 W.", "Vyber možnost C."], "text": "Answer: 48 W\nSteps:\n1. P = 12 V × 4 A.\n2. P = 48 W.\n3. Vyber možnost C.\nAnswer: (C)"}
{"id": "phy_0795", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Proč tepelné stroje?", "choices": null, "answer": "Mění tok tepla v práci.", "steps": ["Mění tok tepla v práci.", "Odpověď tedy platí: Mění tok tepla v práci."], "text": "Answer: Mění tok tepla v práci.\nSteps:\n1. Mění tok tepla v práci.\n2. Odpověď tedy platí: Mění tok tepla v práci."}
{"id": "phy_0796", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why fibre optics?", "choices": null, "answer": "Total reflection pipes light for kilometres, carrying internet globally.", "steps": ["Total reflection pipes light for kilometres, carrying internet globally.", "So the answer stands: Total reflection pipes light for kilometres, carrying internet globally."], "text": "Answer: Total reflection pipes light for kilometres, carrying internet globally.\nSteps:\n1. Total reflection pipes light for kilometres, carrying internet globally.\n2. So the answer stands: Total reflection pipes light for kilometres, carrying internet globally."}
{"id": "phy_0797", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 450 Hz and λ = 2 m. What is its speed?", "choices": {"A": "850 m/s", "B": "950 m/s", "C": "1000 m/s", "D": "900 m/s"}, "answer": "Speed is 900 m/s.", "steps": ["v = 450 Hz × 2 m.", "v = 900 m/s.", "Select option D."], "text": "Answer: 900 m/s\nSteps:\n1. v = 450 Hz × 2 m.\n2. v = 900 m/s.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0798", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Proč kvantování?", "choices": null, "answer": "Vázané soustavy dovolují jen žebřík energií.", "steps": ["Vázané soustavy dovolují jen žebřík energií.", "Odpověď tedy platí: Vázané soustavy dovolují jen žebřík energií."], "text": "Answer: Vázané soustavy dovolují jen žebřík energií.\nSteps:\n1. Vázané soustavy dovolují jen žebřík energií.\n2. Odpověď tedy platí: Vázané soustavy dovolují jen žebřík energií."}
{"id": "phy_0799", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is Kepler's third law?", "choices": null, "answer": "Orbital period squared scales with distance cubed, timing every planet exactly.", "steps": ["Orbital period squared scales with distance cubed, timing every planet exactly.", "So the answer stands: Orbital period squared scales with distance cubed, timing every planet exactly."], "text": "Answer: Orbital period squared scales with distance cubed, timing every planet exactly.\nSteps:\n1. Orbital period squared scales with distance cubed, timing every planet exactly.\n2. So the answer stands: Orbital period squared scales with distance cubed, timing every planet exactly."}
{"id": "phy_0800", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 40 s. How much charge passes?", "choices": {"A": "160 C", "B": "140 C", "C": "180 C", "D": "200 C"}, "answer": "Charge is 160 C.", "steps": ["Q = 4 A × 40 s.", "Q = 160 C.", "Select option A."], "text": "Answer: 160 C\nSteps:\n1. Q = 4 A × 40 s.\n2. Q = 160 C.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0801", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 27 °C. What is it in kelvin?", "choices": {"A": "299 K", "B": "301 K", "C": "302 K", "D": "300 K"}, "answer": "Temperature is 300 K.", "steps": ["27 °C + 273.", "= 300 K.", "Select option D."], "text": "Answer: 300 K\nSteps:\n1. 27 °C + 273.\n2. = 300 K.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0802", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 135 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "85 cm", "B": "90 cm", "C": "95 cm", "D": "100 cm"}, "answer": "Apparent depth is 90 cm.", "steps": ["d' = 135 cm / 1.5.", "d' = 90 cm.", "Select option B."], "text": "Answer: 90 cm\nSteps:\n1. d' = 135 cm / 1.5.\n2. d' = 90 cm.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0803", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 9 Hz. What is its period?", "choices": {"A": "0.11 s", "B": "0.1 s", "C": "0.09 s", "D": "0.12 s"}, "answer": "Period is 0.11 s.", "steps": ["T = 1 / 9 Hz.", "T = 0.11 s.", "Select option A."], "text": "Answer: 0.11 s\nSteps:\n1. T = 1 / 9 Hz.\n2. T = 0.11 s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0804", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 17 protons and 18 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 35.", "steps": ["A = Z+N.", "A = 17 + 18.", "= 35."], "text": "Answer: Mass number: 35.\nSteps:\n1. A = Z+N.\n2. A = 17 + 18.\n3. = 35."}
{"id": "phy_0805", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 18 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 54 kg·m/s.", "steps": ["p = m×v.", "p = 18 kg × 3 m/s.", "= 54 kg·m/s."], "text": "Answer: Momentum: 54 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 18 kg × 3 m/s.\n3. = 54 kg·m/s."}
{"id": "phy_0806", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 19 s. Compute the energy used.", "choices": null, "answer": "Energy: 1900 J.", "steps": ["E = P×t.", "E = 100 W × 19 s.", "= 1900 J."], "text": "Answer: Energy: 1900 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 19 s.\n3. = 1900 J."}
{"id": "phy_0807", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "concept", "question": "Co je entropie?", "choices": null, "answer": "Entropie počítá mikroskopický nepořádek.", "steps": ["Entropie počítá mikroskopický nepořádek.", "Odpověď tedy platí: Entropie počítá mikroskopický nepořádek."], "text": "Answer: Entropie počítá mikroskopický nepořádek.\nSteps:\n1. Entropie počítá mikroskopický nepořádek.\n2. Odpověď tedy platí: Entropie počítá mikroskopický nepořádek."}
{"id": "phy_0808", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "concept", "question": "Proč duha?", "choices": null, "answer": "Kapky lámou a odrážejí světlo pod 42 stupni.", "steps": ["Kapky lámou a odrážejí světlo pod 42 stupni.", "Odpověď tedy platí: Kapky lámou a odrážejí světlo pod 42 stupni."], "text": "Answer: Kapky lámou a odrážejí světlo pod 42 stupni.\nSteps:\n1. Kapky lámou a odrážejí světlo pod 42 stupni.\n2. Odpověď tedy platí: Kapky lámou a odrážejí světlo pod 42 stupni."}
{"id": "phy_0809", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why Cherenkov glow?", "choices": null, "answer": "Particles outpacing light in water trail blue optical booms.", "steps": ["Particles outpacing light in water trail blue optical booms.", "So the answer stands: Particles outpacing light in water trail blue optical booms."], "text": "Answer: Particles outpacing light in water trail blue optical booms.\nSteps:\n1. Particles outpacing light in water trail blue optical booms.\n2. So the answer stands: Particles outpacing light in water trail blue optical booms."}
{"id": "phy_0810", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Co je radioaktivita?", "choices": null, "answer": "Nestabilní jádra se rozpadají s poločasy.", "steps": ["Nestabilní jádra se rozpadají s poločasy.", "Odpověď tedy platí: Nestabilní jádra se rozpadají s poločasy."], "text": "Answer: Nestabilní jádra se rozpadají s poločasy.\nSteps:\n1. Nestabilní jádra se rozpadají s poločasy.\n2. Odpověď tedy platí: Nestabilní jádra se rozpadají s poločasy."}
{"id": "phy_0811", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why tides?", "choices": null, "answer": "The Moon's uneven pull bulges oceans twice daily, dragging high waters around.", "steps": ["The Moon's uneven pull bulges oceans twice daily, dragging high waters around.", "So the answer stands: The Moon's uneven pull bulges oceans twice daily, dragging high waters around."], "text": "Answer: The Moon's uneven pull bulges oceans twice daily, dragging high waters around.\nSteps:\n1. The Moon's uneven pull bulges oceans twice daily, dragging high waters around.\n2. So the answer stands: The Moon's uneven pull bulges oceans twice daily, dragging high waters around."}
{"id": "phy_0812", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Topidlo 100 W běží po 8 s. Spočítej spotřebovanou energii.", "choices": null, "answer": "Energie: 800 J.", "steps": ["E = P×t.", "E = 100 W × 8 s.", "= 800 J."], "text": "Answer: Energie: 800 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 8 s.\n3. = 800 J."}
{"id": "phy_0813", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is Wien's law?", "choices": null, "answer": "Peak wavelength shrinks as temperature rises, from red coals to blue stars.", "steps": ["Peak wavelength shrinks as temperature rises, from red coals to blue stars.", "So the answer stands: Peak wavelength shrinks as temperature rises, from red coals to blue stars."], "text": "Answer: Peak wavelength shrinks as temperature rises, from red coals to blue stars.\nSteps:\n1. Peak wavelength shrinks as temperature rises, from red coals to blue stars.\n2. So the answer stands: Peak wavelength shrinks as temperature rises, from red coals to blue stars."}
{"id": "phy_0814", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is the eye?", "choices": null, "answer": "A living camera focusing light onto retinas with lens and iris.", "steps": ["A living camera focusing light onto retinas with lens and iris.", "So the answer stands: A living camera focusing light onto retinas with lens and iris."], "text": "Answer: A living camera focusing light onto retinas with lens and iris.\nSteps:\n1. A living camera focusing light onto retinas with lens and iris.\n2. So the answer stands: A living camera focusing light onto retinas with lens and iris."}
{"id": "phy_0815", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 240 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 720 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 240 Hz.", "= 720 Hz."], "text": "Answer: 3rd harmonic: 720 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 240 Hz.\n3. = 720 Hz."}
{"id": "phy_0816", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 12800 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 3200.", "steps": ["Halve: 12800 → 6400.", "Halve: 6400 → 3200.", "= 3200."], "text": "Answer: Survivors: 3200.\nSteps:\n1. Halve: 12800 → 6400.\n2. Halve: 6400 → 3200.\n3. = 3200."}
{"id": "phy_0817", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 17 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 34 N.", "steps": ["F = m×a.", "F = 17 kg × 2 m/s².", "= 34 N."], "text": "Answer: Net force: 34 N.\nSteps:\n1. F = m×a.\n2. F = 17 kg × 2 m/s².\n3. = 34 N."}
{"id": "phy_0818", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 5 A teče přes 3 Ω. Spočítej ztrátový výkon.", "choices": null, "answer": "Výkon: 75 W.", "steps": ["P = I²×R.", "P = (5 A)² × 3 Ω.", "= 75 W."], "text": "Answer: Výkon: 75 W.\nSteps:\n1. P = I²×R.\n2. P = (5 A)² × 3 Ω.\n3. = 75 W."}
{"id": "phy_0819", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 9 K? (c = 4186 J/(kg·K))", "choices": {"A": "37674 J", "B": "33488 J", "C": "41860 J", "D": "46046 J"}, "answer": "Heat needed is 37674 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 9 K.", "Q = 37674 J.", "Select option A."], "text": "Answer: 37674 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 9 K.\n2. Q = 37674 J.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0820", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 100 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "10×", "B": "9×", "C": "11×", "D": "12×"}, "answer": "Magnification is 10×.", "steps": ["M = 100 cm / 10 cm.", "M = 10×.", "Select option A."], "text": "Answer: 10×\nSteps:\n1. M = 100 cm / 10 cm.\n2. M = 10×.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0821", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 180 Hz. What is its 3rd harmonic?", "choices": {"A": "510 Hz", "B": "540 Hz", "C": "570 Hz", "D": "600 Hz"}, "answer": "3rd harmonic is 540 Hz.", "steps": ["f3 = 3 × 180 Hz.", "f3 = 540 Hz.", "Select option B."], "text": "Answer: 540 Hz\nSteps:\n1. f3 = 3 × 180 Hz.\n2. f3 = 540 Hz.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0822", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 19. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 171.", "steps": ["Pairs: 19×18/2.", "= 342/2.", "= 171."], "text": "Answer: Lines: 171.\nSteps:\n1. Pairs: 19×18/2.\n2. = 342/2.\n3. = 171."}
{"id": "phy_0823", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 80 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 320 J.", "steps": ["W = F×d.", "W = 80 N × 4 m.", "= 320 J."], "text": "Answer: Work: 320 J.\nSteps:\n1. W = F×d.\n2. W = 80 N × 4 m.\n3. = 320 J."}
{"id": "phy_0824", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why eddy currents?", "choices": null, "answer": "Swirling induced currents brake trains and heat induction stoves.", "steps": ["Swirling induced currents brake trains and heat induction stoves.", "So the answer stands: Swirling induced currents brake trains and heat induction stoves."], "text": "Answer: Swirling induced currents brake trains and heat induction stoves.\nSteps:\n1. Swirling induced currents brake trains and heat induction stoves.\n2. So the answer stands: Swirling induced currents brake trains and heat induction stoves."}
{"id": "phy_0825", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 900 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "80%", "B": "90%", "C": "100%", "D": "110%"}, "answer": "Efficiency is 90%.", "steps": ["900 J / 1000 J.", "= 90%.", "Select option B."], "text": "Answer: 90%\nSteps:\n1. 900 J / 1000 J.\n2. = 90%.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0826", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 240 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 160 cm.", "steps": ["d' = d/n.", "d' = 240 cm / 1.5.", "= 160 cm."], "text": "Answer: Apparent depth: 160 cm.\nSteps:\n1. d' = d/n.\n2. d' = 240 cm / 1.5.\n3. = 160 cm."}
{"id": "phy_0827", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What are gravitational waves?", "choices": null, "answer": "Rippling spacetime from colliding black holes, detected by LIGO.", "steps": ["Rippling spacetime from colliding black holes, detected by LIGO.", "So the answer stands: Rippling spacetime from colliding black holes, detected by LIGO."], "text": "Answer: Rippling spacetime from colliding black holes, detected by LIGO.\nSteps:\n1. Rippling spacetime from colliding black holes, detected by LIGO.\n2. So the answer stands: Rippling spacetime from colliding black holes, detected by LIGO."}
{"id": "phy_0828", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 8. How many spectral lines can it emit?", "choices": {"A": "27", "B": "29", "C": "28", "D": "30"}, "answer": "Count: 28.", "steps": ["Pairs: 8×7/2.", "Lines: 28.", "Select option C."], "text": "Answer: 28\nSteps:\n1. Pairs: 8×7/2.\n2. Lines: 28.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0829", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is terminal velocity?", "choices": null, "answer": "Falling drag grows with speed until balancing weight, capping fall rate steadily.", "steps": ["Falling drag grows with speed until balancing weight, capping fall rate steadily.", "So the answer stands: Falling drag grows with speed until balancing weight, capping fall rate steadily."], "text": "Answer: Falling drag grows with speed until balancing weight, capping fall rate steadily.\nSteps:\n1. Falling drag grows with speed until balancing weight, capping fall rate steadily.\n2. So the answer stands: Falling drag grows with speed until balancing weight, capping fall rate steadily."}
{"id": "phy_0830", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 16 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 768 W.", "steps": ["P = I²×R.", "P = (16 A)² × 3 Ω.", "= 768 W."], "text": "Answer: Power: 768 W.\nSteps:\n1. P = I²×R.\n2. P = (16 A)² × 3 Ω.\n3. = 768 W."}
{"id": "phy_0831", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 28 °C. What is it in kelvin?", "choices": {"A": "301 K", "B": "300 K", "C": "302 K", "D": "303 K"}, "answer": "Temperature is 301 K.", "steps": ["28 °C + 273.", "= 301 K.", "Select option A."], "text": "Answer: 301 K\nSteps:\n1. 28 °C + 273.\n2. = 301 K.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0832", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 27×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "10 s", "B": "9 s", "C": "11 s", "D": "8 s"}, "answer": "Time is 9 s.", "steps": ["t = 27×10⁸ m / 3×10⁸ m/s.", "t = 9 s.", "Select option B."], "text": "Answer: 9 s\nSteps:\n1. t = 27×10⁸ m / 3×10⁸ m/s.\n2. t = 9 s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0833", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 950 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 2850 m/s.", "steps": ["v = f×λ.", "v = 950 Hz × 3 m.", "= 2850 m/s."], "text": "Answer: Speed: 2850 m/s.\nSteps:\n1. v = f×λ.\n2. v = 950 Hz × 3 m.\n3. = 2850 m/s."}
{"id": "phy_0834", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why Pauli exclusion?", "choices": null, "answer": "No two fermions share one state, building chemistry's table.", "steps": ["No two fermions share one state, building chemistry's table.", "So the answer stands: No two fermions share one state, building chemistry's table."], "text": "Answer: No two fermions share one state, building chemistry's table.\nSteps:\n1. No two fermions share one state, building chemistry's table.\n2. So the answer stands: No two fermions share one state, building chemistry's table."}
{"id": "phy_0835", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 10 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "30 N", "B": "27 N", "C": "33 N", "D": "36 N"}, "answer": "Net force is 30 N.", "steps": ["F = 10 kg × 3 m/s².", "F = 30 N.", "Select option A."], "text": "Answer: 30 N\nSteps:\n1. F = 10 kg × 3 m/s².\n2. F = 30 N.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0836", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 9 A flows through 5 Ω. What is the voltage?", "choices": {"A": "40 V", "B": "50 V", "C": "55 V", "D": "45 V"}, "answer": "Voltage is 45 V.", "steps": ["V = 9 A × 5 Ω.", "V = 45 V.", "Select option D."], "text": "Answer: 45 V\nSteps:\n1. V = 9 A × 5 Ω.\n2. V = 45 V.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0837", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why greenhouse effect?", "choices": null, "answer": "Glass passes sunlight but traps infrared, warming planets and houses.", "steps": ["Glass passes sunlight but traps infrared, warming planets and houses.", "So the answer stands: Glass passes sunlight but traps infrared, warming planets and houses."], "text": "Answer: Glass passes sunlight but traps infrared, warming planets and houses.\nSteps:\n1. Glass passes sunlight but traps infrared, warming planets and houses.\n2. So the answer stands: Glass passes sunlight but traps infrared, warming planets and houses."}
{"id": "phy_0838", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 150 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "95 cm", "B": "105 cm", "C": "100 cm", "D": "110 cm"}, "answer": "Apparent depth is 100 cm.", "steps": ["d' = 150 cm / 1.5.", "d' = 100 cm.", "Select option C."], "text": "Answer: 100 cm\nSteps:\n1. d' = 150 cm / 1.5.\n2. d' = 100 cm.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0839", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Základ struny je 120 Hz. Spočítej její 3. harmonickou.", "choices": null, "answer": "3. harmonická: 360 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 120 Hz.", "= 360 Hz."], "text": "Answer: 3. harmonická: 360 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 120 Hz.\n3. = 360 Hz."}
{"id": "phy_0840", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 18 protons and 19 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 37.", "steps": ["A = Z+N.", "A = 18 + 19.", "= 37."], "text": "Answer: Mass number: 37.\nSteps:\n1. A = Z+N.\n2. A = 18 + 19.\n3. = 37."}
{"id": "phy_0841", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why banked curves?", "choices": null, "answer": "Tilted roads supply inward force from normals, letting cars corner without sliding.", "steps": ["Tilted roads supply inward force from normals, letting cars corner without sliding.", "So the answer stands: Tilted roads supply inward force from normals, letting cars corner without sliding."], "text": "Answer: Tilted roads supply inward force from normals, letting cars corner without sliding.\nSteps:\n1. Tilted roads supply inward force from normals, letting cars corner without sliding.\n2. So the answer stands: Tilted roads supply inward force from normals, letting cars corner without sliding."}
{"id": "phy_0842", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 10 A. What is its power?", "choices": {"A": "120 W", "B": "108 W", "C": "132 W", "D": "144 W"}, "answer": "Power is 120 W.", "steps": ["P = 12 V × 10 A.", "P = 120 W.", "Select option A."], "text": "Answer: 120 W\nSteps:\n1. P = 12 V × 10 A.\n2. P = 120 W.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0843", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is a heat pump?", "choices": null, "answer": "It moves more heat than work spent, heating homes efficiently.", "steps": ["It moves more heat than work spent, heating homes efficiently.", "So the answer stands: It moves more heat than work spent, heating homes efficiently."], "text": "Answer: It moves more heat than work spent, heating homes efficiently.\nSteps:\n1. It moves more heat than work spent, heating homes efficiently.\n2. So the answer stands: It moves more heat than work spent, heating homes efficiently."}
{"id": "phy_0844", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 170 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 17×.", "steps": ["M = di/do.", "M = 170 cm / 10 cm.", "= 17×."], "text": "Answer: Magnification: 17×.\nSteps:\n1. M = di/do.\n2. M = 170 cm / 10 cm.\n3. = 17×."}
{"id": "phy_0845", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 17 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 5780 m.", "steps": ["d = v×t.", "d = 340 m/s × 17 s.", "= 5780 m."], "text": "Answer: Distance: 5780 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 17 s.\n3. = 5780 m."}
{"id": "phy_0846", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 7 protons and 7 neutrons. What is its mass number?", "choices": {"A": "13", "B": "15", "C": "16", "D": "14"}, "answer": "Mass number is 14.", "steps": ["A = 7 + 7.", "A = 14.", "Select option D."], "text": "Answer: 14\nSteps:\n1. A = 7 + 7.\n2. A = 14.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0847", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 180 m in 10 s. What is its speed?", "choices": {"A": "17 m/s", "B": "18 m/s", "C": "19 m/s", "D": "20 m/s"}, "answer": "Speed is 18 m/s.", "steps": ["v = 180 m / 10 s.", "v = 18 m/s.", "Select option B."], "text": "Answer: 18 m/s\nSteps:\n1. v = 180 m / 10 s.\n2. v = 18 m/s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0848", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Proud 5 A teče přes 12 Ω. Spočítej napětí.", "choices": null, "answer": "Napětí: 60 V.", "steps": ["U = I×R.", "U = 5 A × 12 Ω.", "= 60 V."], "text": "Answer: Napětí: 60 V.\nSteps:\n1. U = I×R.\n2. U = 5 A × 12 Ω.\n3. = 60 V."}
{"id": "phy_0849", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 15 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 125580 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 15 K.", "= 125580 J."], "text": "Answer: Heat: 125580 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 15 K.\n2. = 125580 J."}
{"id": "phy_0850", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co se ohýbá na rozhraní?", "choices": {"A": "lom", "B": "odraz", "C": "vyvržení", "D": "vstříknutí"}, "answer": "Odpověď je lom.", "steps": ["Rychlosti se liší.", "Tedy: lom.", "Vyber možnost A."], "text": "Answer: lom\nSteps:\n1. Rychlosti se liší.\n2. Tedy: lom.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0851", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Co je rezonance?", "choices": null, "answer": "Sladěné buzení buduje obrovské kmitání.", "steps": ["Sladěné buzení buduje obrovské kmitání.", "Odpověď tedy platí: Sladěné buzení buduje obrovské kmitání."], "text": "Answer: Sladěné buzení buduje obrovské kmitání.\nSteps:\n1. Sladěné buzení buduje obrovské kmitání.\n2. Odpověď tedy platí: Sladěné buzení buduje obrovské kmitání."}
{"id": "phy_0852", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is the Casimir effect?", "choices": null, "answer": "Vacuum fluctuations push close plates together measurably.", "steps": ["Vacuum fluctuations push close plates together measurably.", "So the answer stands: Vacuum fluctuations push close plates together measurably."], "text": "Answer: Vacuum fluctuations push close plates together measurably.\nSteps:\n1. Vacuum fluctuations push close plates together measurably.\n2. So the answer stands: Vacuum fluctuations push close plates together measurably."}
{"id": "phy_0853", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Míč 2 kg letí 5 m/s. Jaká je jeho kinetická energie?", "choices": {"A": "20 J", "B": "30 J", "C": "35 J", "D": "25 J"}, "answer": "Kinetická energie je 25 J.", "steps": ["KE = ½×2 kg×(5 m/s)².", "KE = 25 J.", "Vyber možnost D."], "text": "Answer: 25 J\nSteps:\n1. KE = ½×2 kg×(5 m/s)².\n2. KE = 25 J.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0854", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 45 s. How much charge passes?", "choices": {"A": "160 C", "B": "180 C", "C": "200 C", "D": "220 C"}, "answer": "Charge is 180 C.", "steps": ["Q = 4 A × 45 s.", "Q = 180 C.", "Select option B."], "text": "Answer: 180 C\nSteps:\n1. Q = 4 A × 45 s.\n2. Q = 180 C.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0855", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Kolik tepla ohřeje 2 kg vody o 4 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Teplo: 33488 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 4 K.", "= 33488 J."], "text": "Answer: Teplo: 33488 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 4 K.\n2. = 33488 J."}
{"id": "phy_0856", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An image forms 110 cm from a lens, object at 10 cm. What is the magnification?", "choices": {"A": "10×", "B": "11×", "C": "12×", "D": "13×"}, "answer": "Magnification is 11×.", "steps": ["M = 110 cm / 10 cm.", "M = 11×.", "Select option B."], "text": "Answer: 11×\nSteps:\n1. M = 110 cm / 10 cm.\n2. M = 11×.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0857", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 500 Hz and λ = 2 m. What is its speed?", "choices": {"A": "1000 m/s", "B": "950 m/s", "C": "1050 m/s", "D": "1100 m/s"}, "answer": "Speed is 1000 m/s.", "steps": ["v = 500 Hz × 2 m.", "v = 1000 m/s.", "Select option A."], "text": "Answer: 1000 m/s\nSteps:\n1. v = 500 Hz × 2 m.\n2. v = 1000 m/s.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0858", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 13600 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 3400.", "steps": ["Halve: 13600 → 6800.", "Halve: 6800 → 3400.", "= 3400."], "text": "Answer: Survivors: 3400.\nSteps:\n1. Halve: 13600 → 6800.\n2. Halve: 6800 → 3400.\n3. = 3400."}
{"id": "phy_0859", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 19 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 57 kg·m/s.", "steps": ["p = m×v.", "p = 19 kg × 3 m/s.", "= 57 kg·m/s."], "text": "Answer: Momentum: 57 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 19 kg × 3 m/s.\n3. = 57 kg·m/s."}
{"id": "phy_0860", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Proud 4 A teče po 15 s. Kolik náboje projde?", "choices": {"A": "40 C", "B": "80 C", "C": "100 C", "D": "60 C"}, "answer": "Náboj je 60 C.", "steps": ["Q = 4 A × 15 s.", "Q = 60 C.", "Vyber možnost D."], "text": "Answer: 60 C\nSteps:\n1. Q = 4 A × 15 s.\n2. Q = 60 C.\n3. Vyber možnost D.\nAnswer: (D)"}
{"id": "phy_0861", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 1900 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 190 W.", "steps": ["P = W/t.", "P = 1900 J / 10 s.", "= 190 W."], "text": "Answer: Power: 190 W.\nSteps:\n1. P = W/t.\n2. P = 1900 J / 10 s.\n3. = 190 W."}
{"id": "phy_0862", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 46×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 15.3 s.", "steps": ["t = d/c.", "t = 46×10⁸ / 3×10⁸ s.", "= 15.3 s."], "text": "Answer: Time: 15.3 s.\nSteps:\n1. t = d/c.\n2. t = 46×10⁸ / 3×10⁸ s.\n3. = 15.3 s."}
{"id": "phy_0863", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Vlna na struně má f = 350 Hz a λ = 3 m. Spočítej její rychlost.", "choices": null, "answer": "Rychlost: 1050 m/s.", "steps": ["v = f×λ.", "v = 350 Hz × 3 m.", "= 1050 m/s."], "text": "Answer: Rychlost: 1050 m/s.\nSteps:\n1. v = f×λ.\n2. v = 350 Hz × 3 m.\n3. = 1050 m/s."}
{"id": "phy_0864", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 20. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 190.", "steps": ["Pairs: 20×19/2.", "= 380/2.", "= 190."], "text": "Answer: Lines: 190.\nSteps:\n1. Pairs: 20×19/2.\n2. = 380/2.\n3. = 190."}
{"id": "phy_0865", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co váže tlak a pohyb?", "choices": {"A": "F rovná se ma", "B": "E rovná se mc", "C": "V rovná se IR", "D": "pV rovná se nRT"}, "answer": "Odpověď je F rovná se ma.", "steps": ["Druhý zákon váže.", "Tedy: F rovná se ma.", "Vyber možnost A."], "text": "Answer: F rovná se ma\nSteps:\n1. Druhý zákon váže.\n2. Tedy: F rovná se ma.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0866", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is skin effect?", "choices": null, "answer": "High frequencies crowd to surfaces, raising effective AC resistance.", "steps": ["High frequencies crowd to surfaces, raising effective AC resistance.", "So the answer stands: High frequencies crowd to surfaces, raising effective AC resistance."], "text": "Answer: High frequencies crowd to surfaces, raising effective AC resistance.\nSteps:\n1. High frequencies crowd to surfaces, raising effective AC resistance.\n2. So the answer stands: High frequencies crowd to surfaces, raising effective AC resistance."}
{"id": "phy_0867", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Motor vykoná 800 J práce za 10 s. Spočítej jeho výkon.", "choices": null, "answer": "Výkon: 80 W.", "steps": ["P = W/t.", "P = 800 J / 10 s.", "= 80 W."], "text": "Answer: Výkon: 80 W.\nSteps:\n1. P = W/t.\n2. P = 800 J / 10 s.\n3. = 80 W."}
{"id": "phy_0868", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co dokazuje vlnění?", "choices": {"A": "odraz", "B": "difrakce", "C": "pohlcení", "D": "emise"}, "answer": "Odpověď je difrakce.", "steps": ["Okraje třásněny.", "Tedy: difrakce.", "Vyber možnost B."], "text": "Answer: difrakce\nSteps:\n1. Okraje třásněny.\n2. Tedy: difrakce.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0869", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why LIGO works?", "choices": null, "answer": "Kilometre lasers sense sub-proton arm shifts from passing waves.", "steps": ["Kilometre lasers sense sub-proton arm shifts from passing waves.", "So the answer stands: Kilometre lasers sense sub-proton arm shifts from passing waves."], "text": "Answer: Kilometre lasers sense sub-proton arm shifts from passing waves.\nSteps:\n1. Kilometre lasers sense sub-proton arm shifts from passing waves.\n2. So the answer stands: Kilometre lasers sense sub-proton arm shifts from passing waves."}
{"id": "phy_0870", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 2800 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "650", "B": "750", "C": "700", "D": "800"}, "answer": "700 atoms remain.", "steps": ["Halve twice: 2800 → 1400 → 700.", "Left: 700.", "Select option C."], "text": "Answer: 700\nSteps:\n1. Halve twice: 2800 → 1400 → 700.\n2. Left: 700.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0871", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 18 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 36 N.", "steps": ["F = m×a.", "F = 18 kg × 2 m/s².", "= 36 N."], "text": "Answer: Net force: 36 N.\nSteps:\n1. F = m×a.\n2. F = 18 kg × 2 m/s².\n3. = 36 N."}
{"id": "phy_0872", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 16 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 192 V.", "steps": ["V = I×R.", "V = 16 A × 12 Ω.", "= 192 V."], "text": "Answer: Voltage: 192 V.\nSteps:\n1. V = I×R.\n2. V = 16 A × 12 Ω.\n3. = 192 V."}
{"id": "phy_0873", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 30 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 303 K.", "steps": ["Add 273.", "30 + 273.", "= 303 K."], "text": "Answer: Temperature: 303 K.\nSteps:\n1. Add 273.\n2. 30 + 273.\n3. = 303 K."}
{"id": "phy_0874", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why glasses?", "choices": null, "answer": "Extra lenses correct focus onto retinas, fixing near and far sight.", "steps": ["Extra lenses correct focus onto retinas, fixing near and far sight.", "So the answer stands: Extra lenses correct focus onto retinas, fixing near and far sight."], "text": "Answer: Extra lenses correct focus onto retinas, fixing near and far sight.\nSteps:\n1. Extra lenses correct focus onto retinas, fixing near and far sight.\n2. So the answer stands: Extra lenses correct focus onto retinas, fixing near and far sight."}
{"id": "phy_0875", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 10 Hz. What is its period?", "choices": {"A": "0.09 s", "B": "0.1 s", "C": "0.08 s", "D": "0.11 s"}, "answer": "Period is 0.1 s.", "steps": ["T = 1 / 10 Hz.", "T = 0.1 s.", "Select option B."], "text": "Answer: 0.1 s\nSteps:\n1. T = 1 / 10 Hz.\n2. T = 0.1 s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0876", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 9. How many spectral lines can it emit?", "choices": {"A": "35", "B": "37", "C": "38", "D": "36"}, "answer": "Count: 36.", "steps": ["Pairs: 9×8/2.", "Lines: 36.", "Select option D."], "text": "Answer: 36\nSteps:\n1. Pairs: 9×8/2.\n2. Lines: 36.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0877", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 12 m/s. What is its kinetic energy?", "choices": {"A": "132 J", "B": "156 J", "C": "144 J", "D": "168 J"}, "answer": "Kinetic energy is 144 J.", "steps": ["KE = ½×2 kg×(12 m/s)².", "KE = 144 J.", "Select option C."], "text": "Answer: 144 J\nSteps:\n1. KE = ½×2 kg×(12 m/s)².\n2. KE = 144 J.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0878", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 20 s. Compute the energy used.", "choices": null, "answer": "Energy: 2000 J.", "steps": ["E = P×t.", "E = 100 W × 20 s.", "= 2000 J."], "text": "Answer: Energy: 2000 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 20 s.\n3. = 2000 J."}
{"id": "phy_0879", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Teplota je 19 °C. Převeď ji na kelviny.", "choices": null, "answer": "Teplota: 292 K.", "steps": ["Přičti 273.", "19 + 273.", "= 292 K."], "text": "Answer: Teplota: 292 K.\nSteps:\n1. Přičti 273.\n2. 19 + 273.\n3. = 292 K."}
{"id": "phy_0880", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 255 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 170 cm.", "steps": ["d' = d/n.", "d' = 255 cm / 1.5.", "= 170 cm."], "text": "Answer: Apparent depth: 170 cm.\nSteps:\n1. d' = d/n.\n2. d' = 255 cm / 1.5.\n3. = 170 cm."}
{"id": "phy_0881", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What does the photoelectric effect prove?", "choices": null, "answer": "Light ejects electrons only above threshold frequency, proving photons.", "steps": ["Light ejects electrons only above threshold frequency, proving photons.", "So the answer stands: Light ejects electrons only above threshold frequency, proving photons."], "text": "Answer: Light ejects electrons only above threshold frequency, proving photons.\nSteps:\n1. Light ejects electrons only above threshold frequency, proving photons.\n2. So the answer stands: Light ejects electrons only above threshold frequency, proving photons."}
{"id": "phy_0882", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 19 protons and 20 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 39.", "steps": ["A = Z+N.", "A = 19 + 20.", "= 39."], "text": "Answer: Mass number: 39.\nSteps:\n1. A = Z+N.\n2. A = 19 + 20.\n3. = 39."}
{"id": "phy_0883", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Těleso 7 kg zrychluje 2 m/s². Spočítej výslednou sílu.", "choices": null, "answer": "Výsledná síla: 14 N.", "steps": ["F = m×a.", "F = 7 kg × 2 m/s².", "= 14 N."], "text": "Answer: Výsledná síla: 14 N.\nSteps:\n1. F = m×a.\n2. F = 7 kg × 2 m/s².\n3. = 14 N."}
{"id": "phy_0884", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 17 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 867 W.", "steps": ["P = I²×R.", "P = (17 A)² × 3 Ω.", "= 867 W."], "text": "Answer: Power: 867 W.\nSteps:\n1. P = I²×R.\n2. P = (17 A)² × 3 Ω.\n3. = 867 W."}
{"id": "phy_0885", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why phase diagrams?", "choices": null, "answer": "They map solid-liquid-gas borders versus temperature and pressure.", "steps": ["They map solid-liquid-gas borders versus temperature and pressure.", "So the answer stands: They map solid-liquid-gas borders versus temperature and pressure."], "text": "Answer: They map solid-liquid-gas borders versus temperature and pressure.\nSteps:\n1. They map solid-liquid-gas borders versus temperature and pressure.\n2. So the answer stands: They map solid-liquid-gas borders versus temperature and pressure."}
{"id": "phy_0886", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "Light travels 30×10⁸ m. How many seconds does it take? (c = 3×10⁸ m/s)", "choices": {"A": "11 s", "B": "12 s", "C": "10 s", "D": "9 s"}, "answer": "Time is 10 s.", "steps": ["t = 30×10⁸ m / 3×10⁸ m/s.", "t = 10 s.", "Select option C."], "text": "Answer: 10 s\nSteps:\n1. t = 30×10⁸ m / 3×10⁸ m/s.\n2. t = 10 s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0887", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 250 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 750 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 250 Hz.", "= 750 Hz."], "text": "Answer: 3rd harmonic: 750 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 250 Hz.\n3. = 750 Hz."}
{"id": "phy_0888", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why vacuum energy?", "choices": null, "answer": "Fields jitter even empty, possibly driving cosmic speedup.", "steps": ["Fields jitter even empty, possibly driving cosmic speedup.", "So the answer stands: Fields jitter even empty, possibly driving cosmic speedup."], "text": "Answer: Fields jitter even empty, possibly driving cosmic speedup.\nSteps:\n1. Fields jitter even empty, possibly driving cosmic speedup.\n2. So the answer stands: Fields jitter even empty, possibly driving cosmic speedup."}
{"id": "phy_0889", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 85 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 340 J.", "steps": ["W = F×d.", "W = 85 N × 4 m.", "= 340 J."], "text": "Answer: Work: 340 J.\nSteps:\n1. W = F×d.\n2. W = 85 N × 4 m.\n3. = 340 J."}
{"id": "phy_0890", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 10 A flows through 5 Ω. What is the voltage?", "choices": {"A": "50 V", "B": "45 V", "C": "55 V", "D": "60 V"}, "answer": "Voltage is 50 V.", "steps": ["V = 10 A × 5 Ω.", "V = 50 V.", "Select option A."], "text": "Answer: 50 V\nSteps:\n1. V = 10 A × 5 Ω.\n2. V = 50 V.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0891", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 16 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 133952 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 16 K.", "= 133952 J."], "text": "Answer: Heat: 133952 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 16 K.\n2. = 133952 J."}
{"id": "phy_0892", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 180 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 18×.", "steps": ["M = di/do.", "M = 180 cm / 10 cm.", "= 18×."], "text": "Answer: Magnification: 18×.\nSteps:\n1. M = di/do.\n2. M = 180 cm / 10 cm.\n3. = 18×."}
{"id": "phy_0893", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Hrom je slyšet 5 s po blesku. Jak daleko je bouře? (v = 340 m/s)", "choices": null, "answer": "Vzdálenost: 1700 m.", "steps": ["d = v×t.", "d = 340 m/s × 5 s.", "= 1700 m."], "text": "Answer: Vzdálenost: 1700 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 5 s.\n3. = 1700 m."}
{"id": "phy_0894", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A sample of 14400 atoms undergoes 2 half-lives. Compute the survivors.", "choices": null, "answer": "Survivors: 3600.", "steps": ["Halve: 14400 → 7200.", "Halve: 7200 → 3600.", "= 3600."], "text": "Answer: Survivors: 3600.\nSteps:\n1. Halve: 14400 → 7200.\n2. Halve: 7200 → 3600.\n3. = 3600."}
{"id": "phy_0895", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A mass of 11 kg accelerates at 3 m/s². What is the net force?", "choices": {"A": "30 N", "B": "33 N", "C": "36 N", "D": "39 N"}, "answer": "Net force is 33 N.", "steps": ["F = 11 kg × 3 m/s².", "F = 33 N.", "Select option B."], "text": "Answer: 33 N\nSteps:\n1. F = 11 kg × 3 m/s².\n2. F = 33 N.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0896", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Proč sériově sčítat?", "choices": null, "answer": "Sériové rezistory sdílejí proud, napětí se skládají.", "steps": ["Sériové rezistory sdílejí proud, napětí se skládají.", "Odpověď tedy platí: Sériové rezistory sdílejí proud, napětí se skládají."], "text": "Answer: Sériové rezistory sdílejí proud, napětí se skládají.\nSteps:\n1. Sériové rezistory sdílejí proud, napětí se skládají.\n2. Odpověď tedy platí: Sériové rezistory sdílejí proud, napětí se skládají."}
{"id": "phy_0897", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 10 K? (c = 4186 J/(kg·K))", "choices": {"A": "37674 J", "B": "41860 J", "C": "46046 J", "D": "50232 J"}, "answer": "Heat needed is 41860 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 10 K.", "Q = 41860 J.", "Select option B."], "text": "Answer: 41860 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 10 K.\n2. Q = 41860 J.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0898", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is colour vision?", "choices": null, "answer": "Three cone types mix red, green, blue signals into all hues.", "steps": ["Three cone types mix red, green, blue signals into all hues.", "So the answer stands: Three cone types mix red, green, blue signals into all hues."], "text": "Answer: Three cone types mix red, green, blue signals into all hues.\nSteps:\n1. Three cone types mix red, green, blue signals into all hues.\n2. So the answer stands: Three cone types mix red, green, blue signals into all hues."}
{"id": "phy_0899", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "concept", "question": "Proč stojaté vlnění?", "choices": null, "answer": "Odražené vlny se zamykají do uzlů.", "steps": ["Odražené vlny se zamykají do uzlů.", "Odpověď tedy platí: Odražené vlny se zamykají do uzlů."], "text": "Answer: Odražené vlny se zamykají do uzlů.\nSteps:\n1. Odražené vlny se zamykají do uzlů.\n2. Odpověď tedy platí: Odražené vlny se zamykají do uzlů."}
{"id": "phy_0900", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "An atom is excited to level n = 21. Count the spectral lines it can emit.", "choices": null, "answer": "Lines: 210.", "steps": ["Pairs: 21×20/2.", "= 420/2.", "= 210."], "text": "Answer: Lines: 210.\nSteps:\n1. Pairs: 21×20/2.\n2. = 420/2.\n3. = 210."}
{"id": "phy_0901", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 20 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 60 kg·m/s.", "steps": ["p = m×v.", "p = 20 kg × 3 m/s.", "= 60 kg·m/s."], "text": "Answer: Momentum: 60 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 20 kg × 3 m/s.\n3. = 60 kg·m/s."}
{"id": "phy_0902", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 11 A. What is its power?", "choices": {"A": "120 W", "B": "132 W", "C": "144 W", "D": "156 W"}, "answer": "Power is 132 W.", "steps": ["P = 12 V × 11 A.", "P = 132 W.", "Select option B."], "text": "Answer: 132 W\nSteps:\n1. P = 12 V × 11 A.\n2. P = 132 W.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0903", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 2000 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 200 W.", "steps": ["P = W/t.", "P = 2000 J / 10 s.", "= 200 W."], "text": "Answer: Power: 200 W.\nSteps:\n1. P = W/t.\n2. P = 2000 J / 10 s.\n3. = 200 W."}
{"id": "phy_0904", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why colour blindness?", "choices": null, "answer": "Missing cone types collapse hues, confusing reds with greens.", "steps": ["Missing cone types collapse hues, confusing reds with greens.", "So the answer stands: Missing cone types collapse hues, confusing reds with greens."], "text": "Answer: Missing cone types collapse hues, confusing reds with greens.\nSteps:\n1. Missing cone types collapse hues, confusing reds with greens.\n2. So the answer stands: Missing cone types collapse hues, confusing reds with greens."}
{"id": "phy_0905", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 1000 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 3000 m/s.", "steps": ["v = f×λ.", "v = 1000 Hz × 3 m.", "= 3000 m/s."], "text": "Answer: Speed: 3000 m/s.\nSteps:\n1. v = f×λ.\n2. v = 1000 Hz × 3 m.\n3. = 3000 m/s."}
{"id": "phy_0906", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "worked_example", "question": "Jádro má 6 protonů a 7 neutronů. Spočítej jeho nukleonové číslo.", "choices": null, "answer": "Nukleonové číslo: 13.", "steps": ["A = Z+N.", "A = 6 + 7.", "= 13."], "text": "Answer: Nukleonové číslo: 13.\nSteps:\n1. A = Z+N.\n2. A = 6 + 7.\n3. = 13."}
{"id": "phy_0907", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 19 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 38 N.", "steps": ["F = m×a.", "F = 19 kg × 2 m/s².", "= 38 N."], "text": "Answer: Net force: 38 N.\nSteps:\n1. F = m×a.\n2. F = 19 kg × 2 m/s².\n3. = 38 N."}
{"id": "phy_0908", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 50 s. How much charge passes?", "choices": {"A": "180 C", "B": "220 C", "C": "200 C", "D": "240 C"}, "answer": "Charge is 200 C.", "steps": ["Q = 4 A × 50 s.", "Q = 200 C.", "Select option C."], "text": "Answer: 200 C\nSteps:\n1. Q = 4 A × 50 s.\n2. Q = 200 C.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0909", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 1000 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "90%", "B": "110%", "C": "100%", "D": "120%"}, "answer": "Efficiency is 100%.", "steps": ["1000 J / 1000 J.", "= 100%.", "Select option C."], "text": "Answer: 100%\nSteps:\n1. 1000 J / 1000 J.\n2. = 100%.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0910", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 49×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 16.3 s.", "steps": ["t = d/c.", "t = 49×10⁸ / 3×10⁸ s.", "= 16.3 s."], "text": "Answer: Time: 16.3 s.\nSteps:\n1. t = d/c.\n2. t = 49×10⁸ / 3×10⁸ s.\n3. = 16.3 s."}
{"id": "phy_0911", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 190 Hz. What is its 3rd harmonic?", "choices": {"A": "540 Hz", "B": "600 Hz", "C": "570 Hz", "D": "630 Hz"}, "answer": "3rd harmonic is 570 Hz.", "steps": ["f3 = 3 × 190 Hz.", "f3 = 570 Hz.", "Select option C."], "text": "Answer: 570 Hz\nSteps:\n1. f3 = 3 × 190 Hz.\n2. f3 = 570 Hz.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0912", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 8 protons and 8 neutrons. What is its mass number?", "choices": {"A": "16", "B": "15", "C": "17", "D": "18"}, "answer": "Mass number is 16.", "steps": ["A = 8 + 8.", "A = 16.", "Select option A."], "text": "Answer: 16\nSteps:\n1. A = 8 + 8.\n2. A = 16.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0913", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is the normal force?", "choices": null, "answer": "Surfaces push back perpendicularly exactly as needed, cancelling into-contact forces.", "steps": ["Surfaces push back perpendicularly exactly as needed, cancelling into-contact forces.", "So the answer stands: Surfaces push back perpendicularly exactly as needed, cancelling into-contact forces."], "text": "Answer: Surfaces push back perpendicularly exactly as needed, cancelling into-contact forces.\nSteps:\n1. Surfaces push back perpendicularly exactly as needed, cancelling into-contact forces.\n2. So the answer stands: Surfaces push back perpendicularly exactly as needed, cancelling into-contact forces."}
{"id": "phy_0914", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 17 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 204 V.", "steps": ["V = I×R.", "V = 17 A × 12 Ω.", "= 204 V."], "text": "Answer: Voltage: 204 V.\nSteps:\n1. V = I×R.\n2. V = 17 A × 12 Ω.\n3. = 204 V."}
{"id": "phy_0915", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is critical point?", "choices": null, "answer": "Beyond it liquid and gas merge indistinguishably into supercritical fluid.", "steps": ["Beyond it liquid and gas merge indistinguishably into supercritical fluid.", "So the answer stands: Beyond it liquid and gas merge indistinguishably into supercritical fluid."], "text": "Answer: Beyond it liquid and gas merge indistinguishably into supercritical fluid.\nSteps:\n1. Beyond it liquid and gas merge indistinguishably into supercritical fluid.\n2. So the answer stands: Beyond it liquid and gas merge indistinguishably into supercritical fluid."}
{"id": "phy_0916", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is night vision?", "choices": null, "answer": "Rods sense dim light in grey, trading colour for sensitivity.", "steps": ["Rods sense dim light in grey, trading colour for sensitivity.", "So the answer stands: Rods sense dim light in grey, trading colour for sensitivity."], "text": "Answer: Rods sense dim light in grey, trading colour for sensitivity.\nSteps:\n1. Rods sense dim light in grey, trading colour for sensitivity.\n2. So the answer stands: Rods sense dim light in grey, trading colour for sensitivity."}
{"id": "phy_0917", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why photons?", "choices": null, "answer": "Light packets carry E = hf each, explaining spectra and solar cells.", "steps": ["Light packets carry E = hf each, explaining spectra and solar cells.", "So the answer stands: Light packets carry E = hf each, explaining spectra and solar cells."], "text": "Answer: Light packets carry E = hf each, explaining spectra and solar cells.\nSteps:\n1. Light packets carry E = hf each, explaining spectra and solar cells.\n2. So the answer stands: Light packets carry E = hf each, explaining spectra and solar cells."}
{"id": "phy_0918", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "concept", "question": "Proč poločas?", "choices": null, "answer": "Každé období půlí statisticky.", "steps": ["Každé období půlí statisticky.", "Odpověď tedy platí: Každé období půlí statisticky."], "text": "Answer: Každé období půlí statisticky.\nSteps:\n1. Každé období půlí statisticky.\n2. Odpověď tedy platí: Každé období půlí statisticky."}
{"id": "phy_0919", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why apparent weight?", "choices": null, "answer": "Accelerating floors change scale readings, though gravity itself never varies.", "steps": ["Accelerating floors change scale readings, though gravity itself never varies.", "So the answer stands: Accelerating floors change scale readings, though gravity itself never varies."], "text": "Answer: Accelerating floors change scale readings, though gravity itself never varies.\nSteps:\n1. Accelerating floors change scale readings, though gravity itself never varies.\n2. So the answer stands: Accelerating floors change scale readings, though gravity itself never varies."}
{"id": "phy_0920", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 21 s. Compute the energy used.", "choices": null, "answer": "Energy: 2100 J.", "steps": ["E = P×t.", "E = 100 W × 21 s.", "= 2100 J."], "text": "Answer: Energy: 2100 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 21 s.\n3. = 2100 J."}
{"id": "phy_0921", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "Room temperature is 29 °C. What is it in kelvin?", "choices": {"A": "301 K", "B": "302 K", "C": "303 K", "D": "304 K"}, "answer": "Temperature is 302 K.", "steps": ["29 °C + 273.", "= 302 K.", "Select option B."], "text": "Answer: 302 K\nSteps:\n1. 29 °C + 273.\n2. = 302 K.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0922", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 270 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 180 cm.", "steps": ["d' = d/n.", "d' = 270 cm / 1.5.", "= 180 cm."], "text": "Answer: Apparent depth: 180 cm.\nSteps:\n1. d' = d/n.\n2. d' = 270 cm / 1.5.\n3. = 180 cm."}
{"id": "phy_0923", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 18 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 6120 m.", "steps": ["d = v×t.", "d = 340 m/s × 18 s.", "= 6120 m."], "text": "Answer: Distance: 6120 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 18 s.\n3. = 6120 m."}
{"id": "phy_0924", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 3200 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "750", "B": "850", "C": "900", "D": "800"}, "answer": "800 atoms remain.", "steps": ["Halve twice: 3200 → 1600 → 800.", "Left: 800.", "Select option D."], "text": "Answer: 800\nSteps:\n1. Halve twice: 3200 → 1600 → 800.\n2. Left: 800.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0925", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 90 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 360 J.", "steps": ["W = F×d.", "W = 90 N × 4 m.", "= 360 J."], "text": "Answer: Work: 360 J.\nSteps:\n1. W = F×d.\n2. W = 90 N × 4 m.\n3. = 360 J."}
{"id": "phy_0926", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "concept", "question": "Co je indukce?", "choices": null, "answer": "Měnící se tok budí napětí v cívkách.", "steps": ["Měnící se tok budí napětí v cívkách.", "Odpověď tedy platí: Měnící se tok budí napětí v cívkách."], "text": "Answer: Měnící se tok budí napětí v cívkách.\nSteps:\n1. Měnící se tok budí napětí v cívkách.\n2. Odpověď tedy platí: Měnící se tok budí napětí v cívkách."}
{"id": "phy_0927", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why Brownian motion?", "choices": null, "answer": "Jittering pollen proves molecules exist, kicked randomly by fluid hits.", "steps": ["Jittering pollen proves molecules exist, kicked randomly by fluid hits.", "So the answer stands: Jittering pollen proves molecules exist, kicked randomly by fluid hits."], "text": "Answer: Jittering pollen proves molecules exist, kicked randomly by fluid hits.\nSteps:\n1. Jittering pollen proves molecules exist, kicked randomly by fluid hits.\n2. So the answer stands: Jittering pollen proves molecules exist, kicked randomly by fluid hits."}
{"id": "phy_0928", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why adaptive optics?", "choices": null, "answer": "Deforming mirrors cancel air shimmer live, sharpening star images.", "steps": ["Deforming mirrors cancel air shimmer live, sharpening star images.", "So the answer stands: Deforming mirrors cancel air shimmer live, sharpening star images."], "text": "Answer: Deforming mirrors cancel air shimmer live, sharpening star images.\nSteps:\n1. Deforming mirrors cancel air shimmer live, sharpening star images.\n2. So the answer stands: Deforming mirrors cancel air shimmer live, sharpening star images."}
{"id": "phy_0929", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 260 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 780 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 260 Hz.", "= 780 Hz."], "text": "Answer: 3rd harmonic: 780 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 260 Hz.\n3. = 780 Hz."}
{"id": "phy_0930", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 10. How many spectral lines can it emit?", "choices": {"A": "45", "B": "44", "C": "46", "D": "47"}, "answer": "Count: 45.", "steps": ["Pairs: 10×9/2.", "Lines: 45.", "Select option A."], "text": "Answer: 45\nSteps:\n1. Pairs: 10×9/2.\n2. Lines: 45.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0931", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "concept", "question": "Proč moment síly?", "choices": null, "answer": "Moment je síla krát rameno a roztáčí tělesa.", "steps": ["Moment je síla krát rameno a roztáčí tělesa.", "Odpověď tedy platí: Moment je síla krát rameno a roztáčí tělesa."], "text": "Answer: Moment je síla krát rameno a roztáčí tělesa.\nSteps:\n1. Moment je síla krát rameno a roztáčí tělesa.\n2. Odpověď tedy platí: Moment je síla krát rameno a roztáčí tělesa."}
{"id": "phy_0932", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why shield cables?", "choices": null, "answer": "Metal braids block interference, keeping signals clean in noise.", "steps": ["Metal braids block interference, keeping signals clean in noise.", "So the answer stands: Metal braids block interference, keeping signals clean in noise."], "text": "Answer: Metal braids block interference, keeping signals clean in noise.\nSteps:\n1. Metal braids block interference, keeping signals clean in noise.\n2. So the answer stands: Metal braids block interference, keeping signals clean in noise."}
{"id": "phy_0933", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is diffusion?", "choices": null, "answer": "Particles spread from crowded to empty randomly, mixing air and ink.", "steps": ["Particles spread from crowded to empty randomly, mixing air and ink.", "So the answer stands: Particles spread from crowded to empty randomly, mixing air and ink."], "text": "Answer: Particles spread from crowded to empty randomly, mixing air and ink.\nSteps:\n1. Particles spread from crowded to empty randomly, mixing air and ink.\n2. So the answer stands: Particles spread from crowded to empty randomly, mixing air and ink."}
{"id": "phy_0934", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is the speed of light?", "choices": null, "answer": "c is 299792458 m/s exactly, the cosmic limit nothing exceeds.", "steps": ["c is 299792458 m/s exactly, the cosmic limit nothing exceeds.", "So the answer stands: c is 299792458 m/s exactly, the cosmic limit nothing exceeds."], "text": "Answer: c is 299792458 m/s exactly, the cosmic limit nothing exceeds.\nSteps:\n1. c is 299792458 m/s exactly, the cosmic limit nothing exceeds.\n2. So the answer stands: c is 299792458 m/s exactly, the cosmic limit nothing exceeds."}
{"id": "phy_0935", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string wave has f = 1050 Hz and λ = 3 m. Compute its speed.", "choices": null, "answer": "Speed: 3150 m/s.", "steps": ["v = f×λ.", "v = 1050 Hz × 3 m.", "= 3150 m/s."], "text": "Answer: Speed: 3150 m/s.\nSteps:\n1. v = f×λ.\n2. v = 1050 Hz × 3 m.\n3. = 3150 m/s."}
{"id": "phy_0936", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 9 protons and 9 neutrons. What is its mass number?", "choices": {"A": "17", "B": "18", "C": "19", "D": "20"}, "answer": "Mass number is 18.", "steps": ["A = 9 + 9.", "A = 18.", "Select option B."], "text": "Answer: 18\nSteps:\n1. A = 9 + 9.\n2. A = 18.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0937", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is a pulley for?", "choices": null, "answer": "Pulleys redirect tension and share loads, trading pull distance for force ease.", "steps": ["Pulleys redirect tension and share loads, trading pull distance for force ease.", "So the answer stands: Pulleys redirect tension and share loads, trading pull distance for force ease."], "text": "Answer: Pulleys redirect tension and share loads, trading pull distance for force ease.\nSteps:\n1. Pulleys redirect tension and share loads, trading pull distance for force ease.\n2. So the answer stands: Pulleys redirect tension and share loads, trading pull distance for force ease."}
{"id": "phy_0938", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "What is static shock?", "choices": null, "answer": "Separated charges reunite suddenly through air, zapping fingers dryly.", "steps": ["Separated charges reunite suddenly through air, zapping fingers dryly.", "So the answer stands: Separated charges reunite suddenly through air, zapping fingers dryly."], "text": "Answer: Separated charges reunite suddenly through air, zapping fingers dryly.\nSteps:\n1. Separated charges reunite suddenly through air, zapping fingers dryly.\n2. So the answer stands: Separated charges reunite suddenly through air, zapping fingers dryly."}
{"id": "phy_0939", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 31 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 304 K.", "steps": ["Add 273.", "31 + 273.", "= 304 K."], "text": "Answer: Temperature: 304 K.\nSteps:\n1. Add 273.\n2. 31 + 273.\n3. = 304 K."}
{"id": "phy_0940", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why constant c?", "choices": null, "answer": "Relativity holds light speed fixed for all observers, warping time itself.", "steps": ["Relativity holds light speed fixed for all observers, warping time itself.", "So the answer stands: Relativity holds light speed fixed for all observers, warping time itself."], "text": "Answer: Relativity holds light speed fixed for all observers, warping time itself.\nSteps:\n1. Relativity holds light speed fixed for all observers, warping time itself.\n2. So the answer stands: Relativity holds light speed fixed for all observers, warping time itself."}
{"id": "phy_0941", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string wave has f = 550 Hz and λ = 2 m. What is its speed?", "choices": {"A": "1050 m/s", "B": "1100 m/s", "C": "1150 m/s", "D": "1200 m/s"}, "answer": "Speed is 1100 m/s.", "steps": ["v = 550 Hz × 2 m.", "v = 1100 m/s.", "Select option B."], "text": "Answer: 1100 m/s\nSteps:\n1. v = 550 Hz × 2 m.\n2. v = 1100 m/s.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0942", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 3600 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "900", "B": "850", "C": "950", "D": "1000"}, "answer": "900 atoms remain.", "steps": ["Halve twice: 3600 → 1800 → 900.", "Left: 900.", "Select option A."], "text": "Answer: 900\nSteps:\n1. Halve twice: 3600 → 1800 → 900.\n2. Left: 900.\n3. Select option A.\nAnswer: (A)"}
{"id": "phy_0943", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 21 kg moves at 3 m/s. Compute its momentum.", "choices": null, "answer": "Momentum: 63 kg·m/s.", "steps": ["p = m×v.", "p = 21 kg × 3 m/s.", "= 63 kg·m/s."], "text": "Answer: Momentum: 63 kg·m/s.\nSteps:\n1. p = m×v.\n2. p = 21 kg × 3 m/s.\n3. = 63 kg·m/s."}
{"id": "phy_0944", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "concept", "question": "Why study electromagnetism?", "choices": null, "answer": "It powers civilization from lights to chips, unifying forces elegantly.", "steps": ["It powers civilization from lights to chips, unifying forces elegantly.", "So the answer stands: It powers civilization from lights to chips, unifying forces elegantly."], "text": "Answer: It powers civilization from lights to chips, unifying forces elegantly.\nSteps:\n1. It powers civilization from lights to chips, unifying forces elegantly.\n2. So the answer stands: It powers civilization from lights to chips, unifying forces elegantly."}
{"id": "phy_0945", "subject": "physics", "topic": "thermodynamics", "lang": "cs", "kind": "worked_example", "question": "Kolik tepla ohřeje 2 kg vody o 5 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Teplo: 41860 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 5 K.", "= 41860 J."], "text": "Answer: Teplo: 41860 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 5 K.\n2. = 41860 J."}
{"id": "phy_0946", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 190 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 19×.", "steps": ["M = di/do.", "M = 190 cm / 10 cm.", "= 19×."], "text": "Answer: Magnification: 19×.\nSteps:\n1. M = di/do.\n2. M = 190 cm / 10 cm.\n3. = 19×."}
{"id": "phy_0947", "subject": "physics", "topic": "waves", "lang": "cs", "kind": "worked_example", "question": "Základ struny je 130 Hz. Spočítej její 3. harmonickou.", "choices": null, "answer": "3. harmonická: 390 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 130 Hz.", "= 390 Hz."], "text": "Answer: 3. harmonická: 390 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 130 Hz.\n3. = 390 Hz."}
{"id": "phy_0948", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 11. How many spectral lines can it emit?", "choices": {"A": "54", "B": "55", "C": "56", "D": "57"}, "answer": "Count: 55.", "steps": ["Pairs: 11×10/2.", "Lines: 55.", "Select option B."], "text": "Answer: 55\nSteps:\n1. Pairs: 11×10/2.\n2. Lines: 55.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0949", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A mass of 20 kg accelerates at 2 m/s². Compute the net force.", "choices": null, "answer": "Net force: 40 N.", "steps": ["F = m×a.", "F = 20 kg × 2 m/s².", "= 40 N."], "text": "Answer: Net force: 40 N.\nSteps:\n1. F = m×a.\n2. F = 20 kg × 2 m/s².\n3. = 40 N."}
{"id": "phy_0950", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 18 A flows through 3 Ω. Compute the dissipated power.", "choices": null, "answer": "Power: 972 W.", "steps": ["P = I²×R.", "P = (18 A)² × 3 Ω.", "= 972 W."], "text": "Answer: Power: 972 W.\nSteps:\n1. P = I²×R.\n2. P = (18 A)² × 3 Ω.\n3. = 972 W."}
{"id": "phy_0951", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "How much heat warms 1 kg of water by 11 K? (c = 4186 J/(kg·K))", "choices": {"A": "41860 J", "B": "50232 J", "C": "46046 J", "D": "54418 J"}, "answer": "Heat needed is 46046 J.", "steps": ["Q = 1 kg × 4186 J/(kg·K) × 11 K.", "Q = 46046 J.", "Select option C."], "text": "Answer: 46046 J\nSteps:\n1. Q = 1 kg × 4186 J/(kg·K) × 11 K.\n2. Q = 46046 J.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0952", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Obraz vzniká 70 cm od čočky, předmět v 10 cm. Spočítej zvětšení.", "choices": null, "answer": "Zvětšení: 7×.", "steps": ["M = di/do.", "M = 70 cm / 10 cm.", "= 7×."], "text": "Answer: Zvětšení: 7×.\nSteps:\n1. M = di/do.\n2. M = 70 cm / 10 cm.\n3. = 7×."}
{"id": "phy_0953", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is wave-particle duality?", "choices": null, "answer": "Everything shows both wave and particle faces in experiments.", "steps": ["Everything shows both wave and particle faces in experiments.", "So the answer stands: Everything shows both wave and particle faces in experiments."], "text": "Answer: Everything shows both wave and particle faces in experiments.\nSteps:\n1. Everything shows both wave and particle faces in experiments.\n2. So the answer stands: Everything shows both wave and particle faces in experiments."}
{"id": "phy_0954", "subject": "physics", "topic": "modern", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co slučuje lehké?", "choices": {"A": "zmatek", "B": "fúze", "C": "difuze", "D": "iluze"}, "answer": "Odpověď je fúze.", "steps": ["Hvězdy rozsvíceny.", "Tedy: fúze.", "Vyber možnost B."], "text": "Answer: fúze\nSteps:\n1. Hvězdy rozsvíceny.\n2. Tedy: fúze.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0955", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "worked_example", "question": "A force of 95 N pushes 4 m. Compute the work done.", "choices": null, "answer": "Work: 380 J.", "steps": ["W = F×d.", "W = 95 N × 4 m.", "= 380 J."], "text": "Answer: Work: 380 J.\nSteps:\n1. W = F×d.\n2. W = 95 N × 4 m.\n3. = 380 J."}
{"id": "phy_0956", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A current of 18 A flows through 12 Ω. Compute the voltage.", "choices": null, "answer": "Voltage: 216 V.", "steps": ["V = I×R.", "V = 18 A × 12 Ω.", "= 216 V."], "text": "Answer: Voltage: 216 V.\nSteps:\n1. V = I×R.\n2. V = 18 A × 12 Ω.\n3. = 216 V."}
{"id": "phy_0957", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 17 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 142324 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 17 K.", "= 142324 J."], "text": "Answer: Heat: 142324 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 17 K.\n2. = 142324 J."}
{"id": "phy_0958", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "What is redshift?", "choices": null, "answer": "Stretching space lengthens light waves, revealing cosmic expansion.", "steps": ["Stretching space lengthens light waves, revealing cosmic expansion.", "So the answer stands: Stretching space lengthens light waves, revealing cosmic expansion."], "text": "Answer: Stretching space lengthens light waves, revealing cosmic expansion.\nSteps:\n1. Stretching space lengthens light waves, revealing cosmic expansion.\n2. So the answer stands: Stretching space lengthens light waves, revealing cosmic expansion."}
{"id": "phy_0959", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "Thunder is heard 19 s after lightning. How far away is the storm? (v = 340 m/s)", "choices": null, "answer": "Distance: 6460 m.", "steps": ["d = v×t.", "d = 340 m/s × 19 s.", "= 6460 m."], "text": "Answer: Distance: 6460 m.\nSteps:\n1. d = v×t.\n2. d = 340 m/s × 19 s.\n3. = 6460 m."}
{"id": "phy_0960", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "What is string theory?", "choices": null, "answer": "It models particles as tiny vibrating strings unifying forces.", "steps": ["It models particles as tiny vibrating strings unifying forces.", "So the answer stands: It models particles as tiny vibrating strings unifying forces."], "text": "Answer: It models particles as tiny vibrating strings unifying forces.\nSteps:\n1. It models particles as tiny vibrating strings unifying forces.\n2. So the answer stands: It models particles as tiny vibrating strings unifying forces."}
{"id": "phy_0961", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why gears?", "choices": null, "answer": "Meshed teeth trade speed for torque at fixed ratios, powering machines efficiently.", "steps": ["Meshed teeth trade speed for torque at fixed ratios, powering machines efficiently.", "So the answer stands: Meshed teeth trade speed for torque at fixed ratios, powering machines efficiently."], "text": "Answer: Meshed teeth trade speed for torque at fixed ratios, powering machines efficiently.\nSteps:\n1. Meshed teeth trade speed for torque at fixed ratios, powering machines efficiently.\n2. So the answer stands: Meshed teeth trade speed for torque at fixed ratios, powering machines efficiently."}
{"id": "phy_0962", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 11 A flows through 5 Ω. What is the voltage?", "choices": {"A": "50 V", "B": "55 V", "C": "60 V", "D": "65 V"}, "answer": "Voltage is 55 V.", "steps": ["V = 11 A × 5 Ω.", "V = 55 V.", "Select option B."], "text": "Answer: 55 V\nSteps:\n1. V = 11 A × 5 Ω.\n2. V = 55 V.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0963", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "An engine does 2100 J of work in 10 s. Compute its power.", "choices": null, "answer": "Power: 210 W.", "steps": ["P = W/t.", "P = 2100 J / 10 s.", "= 210 W."], "text": "Answer: Power: 210 W.\nSteps:\n1. P = W/t.\n2. P = 2100 J / 10 s.\n3. = 210 W."}
{"id": "phy_0964", "subject": "physics", "topic": "optics", "lang": "cs", "kind": "worked_example", "question": "Světlo letí 16×10⁸ m. Spočítej dobu letu. (c = 3×10⁸ m/s)", "choices": null, "answer": "Čas: 5,3 s.", "steps": ["t = d/c.", "t = 16×10⁸ / 3×10⁸ s.", "= 5,3 s."], "text": "Answer: Čas: 5,3 s.\nSteps:\n1. t = d/c.\n2. t = 16×10⁸ / 3×10⁸ s.\n3. = 5,3 s."}
{"id": "phy_0965", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A wave has frequency 11 Hz. What is its period?", "choices": {"A": "0.1 s", "B": "0.11 s", "C": "0.09 s", "D": "0.08 s"}, "answer": "Period is 0.09 s.", "steps": ["T = 1 / 11 Hz.", "T = 0.09 s.", "Select option C."], "text": "Answer: 0.09 s\nSteps:\n1. T = 1 / 11 Hz.\n2. T = 0.09 s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0966", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 10 protons and 10 neutrons. What is its mass number?", "choices": {"A": "19", "B": "21", "C": "20", "D": "22"}, "answer": "Mass number is 20.", "steps": ["A = 10 + 10.", "A = 20.", "Select option C."], "text": "Answer: 20\nSteps:\n1. A = 10 + 10.\n2. A = 20.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0967", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "What is the centre of mass?", "choices": null, "answer": "It is the balance point moving as if all mass sat there under net force.", "steps": ["It is the balance point moving as if all mass sat there under net force.", "So the answer stands: It is the balance point moving as if all mass sat there under net force."], "text": "Answer: It is the balance point moving as if all mass sat there under net force.\nSteps:\n1. It is the balance point moving as if all mass sat there under net force.\n2. So the answer stands: It is the balance point moving as if all mass sat there under net force."}
{"id": "phy_0968", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A bulb runs at 12 V drawing 12 A. What is its power?", "choices": {"A": "132 W", "B": "156 W", "C": "144 W", "D": "168 W"}, "answer": "Power is 144 W.", "steps": ["P = 12 V × 12 A.", "P = 144 W.", "Select option C."], "text": "Answer: 144 W\nSteps:\n1. P = 12 V × 12 A.\n2. P = 144 W.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0969", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "multiple_choice", "question": "An engine turns 1100 J of 1000 J heat into work. What is its efficiency?", "choices": {"A": "100%", "B": "120%", "C": "130%", "D": "110%"}, "answer": "Efficiency is 110%.", "steps": ["1100 J / 1000 J.", "= 110%.", "Select option D."], "text": "Answer: 110%\nSteps:\n1. 1100 J / 1000 J.\n2. = 110%.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0970", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 52×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 17.3 s.", "steps": ["t = d/c.", "t = 52×10⁸ / 3×10⁸ s.", "= 17.3 s."], "text": "Answer: Time: 17.3 s.\nSteps:\n1. t = d/c.\n2. t = 52×10⁸ / 3×10⁸ s.\n3. = 17.3 s."}
{"id": "phy_0971", "subject": "physics", "topic": "waves", "lang": "en", "kind": "worked_example", "question": "A string's fundamental is 270 Hz. Compute its 3rd harmonic.", "choices": null, "answer": "3rd harmonic: 810 Hz.", "steps": ["f3 = 3×f1.", "f3 = 3 × 270 Hz.", "= 810 Hz."], "text": "Answer: 3rd harmonic: 810 Hz.\nSteps:\n1. f3 = 3×f1.\n2. f3 = 3 × 270 Hz.\n3. = 810 Hz."}
{"id": "phy_0972", "subject": "physics", "topic": "modern", "lang": "en", "kind": "concept", "question": "Why study modern physics?", "choices": null, "answer": "It reveals deep reality from quanta to cosmos.", "steps": ["It reveals deep reality from quanta to cosmos.", "So the answer stands: It reveals deep reality from quanta to cosmos."], "text": "Answer: It reveals deep reality from quanta to cosmos.\nSteps:\n1. It reveals deep reality from quanta to cosmos.\n2. So the answer stands: It reveals deep reality from quanta to cosmos."}
{"id": "phy_0973", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A car travels 190 m in 10 s. What is its speed?", "choices": {"A": "18 m/s", "B": "20 m/s", "C": "19 m/s", "D": "21 m/s"}, "answer": "Speed is 19 m/s.", "steps": ["v = 190 m / 10 s.", "v = 19 m/s.", "Select option C."], "text": "Answer: 19 m/s\nSteps:\n1. v = 190 m / 10 s.\n2. v = 19 m/s.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0974", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "worked_example", "question": "A 100 W heater runs for 22 s. Compute the energy used.", "choices": null, "answer": "Energy: 2200 J.", "steps": ["E = P×t.", "E = 100 W × 22 s.", "= 2200 J."], "text": "Answer: Energy: 2200 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 22 s.\n3. = 2200 J."}
{"id": "phy_0975", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why osmosis?", "choices": null, "answer": "Solvent crosses membranes toward solute, pressuring cells and roots.", "steps": ["Solvent crosses membranes toward solute, pressuring cells and roots.", "So the answer stands: Solvent crosses membranes toward solute, pressuring cells and roots."], "text": "Answer: Solvent crosses membranes toward solute, pressuring cells and roots.\nSteps:\n1. Solvent crosses membranes toward solute, pressuring cells and roots.\n2. So the answer stands: Solvent crosses membranes toward solute, pressuring cells and roots."}
{"id": "phy_0976", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An object sits 285 cm deep in glass (n = 1.5). Compute the apparent depth.", "choices": null, "answer": "Apparent depth: 190 cm.", "steps": ["d' = d/n.", "d' = 285 cm / 1.5.", "= 190 cm."], "text": "Answer: Apparent depth: 190 cm.\nSteps:\n1. d' = d/n.\n2. d' = 285 cm / 1.5.\n3. = 190 cm."}
{"id": "phy_0977", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why de Broglie?", "choices": null, "answer": "Matter wavelength h/p guides electron microscopes to atoms.", "steps": ["Matter wavelength h/p guides electron microscopes to atoms.", "So the answer stands: Matter wavelength h/p guides electron microscopes to atoms."], "text": "Answer: Matter wavelength h/p guides electron microscopes to atoms.\nSteps:\n1. Matter wavelength h/p guides electron microscopes to atoms.\n2. So the answer stands: Matter wavelength h/p guides electron microscopes to atoms."}
{"id": "phy_0978", "subject": "physics", "topic": "modern", "lang": "en", "kind": "worked_example", "question": "A nucleus has 20 protons and 21 neutrons. Compute its mass number.", "choices": null, "answer": "Mass number: 41.", "steps": ["A = Z+N.", "A = 20 + 21.", "= 41."], "text": "Answer: Mass number: 41.\nSteps:\n1. A = Z+N.\n2. A = 20 + 21.\n3. = 41."}
{"id": "phy_0979", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "concept", "question": "Why study mechanics?", "choices": null, "answer": "It predicts all motion from atoms to galaxies, the foundation of physics.", "steps": ["It predicts all motion from atoms to galaxies, the foundation of physics.", "So the answer stands: It predicts all motion from atoms to galaxies, the foundation of physics."], "text": "Answer: It predicts all motion from atoms to galaxies, the foundation of physics.\nSteps:\n1. It predicts all motion from atoms to galaxies, the foundation of physics.\n2. So the answer stands: It predicts all motion from atoms to galaxies, the foundation of physics."}
{"id": "phy_0980", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co je energie na náboj?", "choices": {"A": "napětí", "B": "proud", "C": "výkon", "D": "síla"}, "answer": "Odpověď je napětí.", "steps": ["Volty tlačí tok.", "Tedy: napětí.", "Vyber možnost A."], "text": "Answer: napětí\nSteps:\n1. Volty tlačí tok.\n2. Tedy: napětí.\n3. Vyber možnost A.\nAnswer: (A)"}
{"id": "phy_0981", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "What is Maxwell distribution?", "choices": null, "answer": "Molecular speeds spread predictably around most-likely values by temperature.", "steps": ["Molecular speeds spread predictably around most-likely values by temperature.", "So the answer stands: Molecular speeds spread predictably around most-likely values by temperature."], "text": "Answer: Molecular speeds spread predictably around most-likely values by temperature.\nSteps:\n1. Molecular speeds spread predictably around most-likely values by temperature.\n2. So the answer stands: Molecular speeds spread predictably around most-likely values by temperature."}
{"id": "phy_0982", "subject": "physics", "topic": "optics", "lang": "en", "kind": "multiple_choice", "question": "An object sits 165 cm deep in glass (n = 1.5). What is the apparent depth?", "choices": {"A": "105 cm", "B": "115 cm", "C": "120 cm", "D": "110 cm"}, "answer": "Apparent depth is 110 cm.", "steps": ["d' = 165 cm / 1.5.", "d' = 110 cm.", "Select option D."], "text": "Answer: 110 cm\nSteps:\n1. d' = 165 cm / 1.5.\n2. d' = 110 cm.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0983", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "What is uncertainty?", "choices": null, "answer": "Position-momentum spread has a quantum floor, blurring tiny scales.", "steps": ["Position-momentum spread has a quantum floor, blurring tiny scales.", "So the answer stands: Position-momentum spread has a quantum floor, blurring tiny scales."], "text": "Answer: Position-momentum spread has a quantum floor, blurring tiny scales.\nSteps:\n1. Position-momentum spread has a quantum floor, blurring tiny scales.\n2. So the answer stands: Position-momentum spread has a quantum floor, blurring tiny scales."}
{"id": "phy_0984", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A sample of 4000 atoms undergoes 2 half-lives. How many remain?", "choices": {"A": "950", "B": "1000", "C": "1050", "D": "1100"}, "answer": "1000 atoms remain.", "steps": ["Halve twice: 4000 → 2000 → 1000.", "Left: 1000.", "Select option B."], "text": "Answer: 1000\nSteps:\n1. Halve twice: 4000 → 2000 → 1000.\n2. Left: 1000.\n3. Select option B.\nAnswer: (B)"}
{"id": "phy_0985", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "worked_example", "question": "Síla 30 N tlačí na dráze 4 m. Spočítej vykonanou práci.", "choices": null, "answer": "Práce: 120 J.", "steps": ["W = F×d.", "W = 30 N × 4 m.", "= 120 J."], "text": "Answer: Práce: 120 J.\nSteps:\n1. W = F×d.\n2. W = 30 N × 4 m.\n3. = 120 J."}
{"id": "phy_0986", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co škáluje závity?", "choices": {"A": "motor", "B": "transformátor", "C": "baterie", "D": "pojistka"}, "answer": "Odpověď je transformátor.", "steps": ["Napětí poměřeno.", "Tedy: transformátor.", "Vyber možnost B."], "text": "Answer: transformátor\nSteps:\n1. Napětí poměřeno.\n2. Tedy: transformátor.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0987", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "Temperature is 32 °C. Convert it to kelvin.", "choices": null, "answer": "Temperature: 305 K.", "steps": ["Add 273.", "32 + 273.", "= 305 K."], "text": "Answer: Temperature: 305 K.\nSteps:\n1. Add 273.\n2. 32 + 273.\n3. = 305 K."}
{"id": "phy_0988", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "An image forms 200 cm from a lens, object at 10 cm. Compute the magnification.", "choices": null, "answer": "Magnification: 20×.", "steps": ["M = di/do.", "M = 200 cm / 10 cm.", "= 20×."], "text": "Answer: Magnification: 20×.\nSteps:\n1. M = di/do.\n2. M = 200 cm / 10 cm.\n3. = 20×."}
{"id": "phy_0989", "subject": "physics", "topic": "waves", "lang": "en", "kind": "multiple_choice", "question": "A string's fundamental is 200 Hz. What is its 3rd harmonic?", "choices": {"A": "570 Hz", "B": "630 Hz", "C": "660 Hz", "D": "600 Hz"}, "answer": "3rd harmonic is 600 Hz.", "steps": ["f3 = 3 × 200 Hz.", "f3 = 600 Hz.", "Select option D."], "text": "Answer: 600 Hz\nSteps:\n1. f3 = 3 × 200 Hz.\n2. f3 = 600 Hz.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0990", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "An atom is excited to level n = 12. How many spectral lines can it emit?", "choices": {"A": "65", "B": "67", "C": "66", "D": "68"}, "answer": "Count: 66.", "steps": ["Pairs: 12×11/2.", "Lines: 66.", "Select option C."], "text": "Answer: 66\nSteps:\n1. Pairs: 12×11/2.\n2. Lines: 66.\n3. Select option C.\nAnswer: (C)"}
{"id": "phy_0991", "subject": "physics", "topic": "mechanics", "lang": "en", "kind": "multiple_choice", "question": "A 2 kg ball moves at 13 m/s. What is its kinetic energy?", "choices": {"A": "156 J", "B": "182 J", "C": "195 J", "D": "169 J"}, "answer": "Kinetic energy is 169 J.", "steps": ["KE = ½×2 kg×(13 m/s)².", "KE = 169 J.", "Select option D."], "text": "Answer: 169 J\nSteps:\n1. KE = ½×2 kg×(13 m/s)².\n2. KE = 169 J.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0992", "subject": "physics", "topic": "electromagnetism", "lang": "cs", "kind": "worked_example", "question": "Topidlo 100 W běží po 9 s. Spočítej spotřebovanou energii.", "choices": null, "answer": "Energie: 900 J.", "steps": ["E = P×t.", "E = 100 W × 9 s.", "= 900 J."], "text": "Answer: Energie: 900 J.\nSteps:\n1. E = P×t.\n2. E = 100 W × 9 s.\n3. = 900 J."}
{"id": "phy_0993", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "worked_example", "question": "How much heat warms 2 kg of water by 18 K? (c = 4186 J/(kg·K))", "choices": null, "answer": "Heat: 150696 J.", "steps": ["Q = 2 kg × 4186 J/(kg·K) × 18 K.", "= 150696 J."], "text": "Answer: Heat: 150696 J.\nSteps:\n1. Q = 2 kg × 4186 J/(kg·K) × 18 K.\n2. = 150696 J."}
{"id": "phy_0994", "subject": "physics", "topic": "optics", "lang": "en", "kind": "concept", "question": "Why study optics?", "choices": null, "answer": "It explains sight, cameras, and cosmos through light's behaviour.", "steps": ["It explains sight, cameras, and cosmos through light's behaviour.", "So the answer stands: It explains sight, cameras, and cosmos through light's behaviour."], "text": "Answer: It explains sight, cameras, and cosmos through light's behaviour.\nSteps:\n1. It explains sight, cameras, and cosmos through light's behaviour.\n2. So the answer stands: It explains sight, cameras, and cosmos through light's behaviour."}
{"id": "phy_0995", "subject": "physics", "topic": "waves", "lang": "en", "kind": "concept", "question": "Why study waves?", "choices": null, "answer": "Waves explain sound, light, and quantum all at once.", "steps": ["Waves explain sound, light, and quantum all at once.", "So the answer stands: Waves explain sound, light, and quantum all at once."], "text": "Answer: Waves explain sound, light, and quantum all at once.\nSteps:\n1. Waves explain sound, light, and quantum all at once.\n2. So the answer stands: Waves explain sound, light, and quantum all at once."}
{"id": "phy_0996", "subject": "physics", "topic": "modern", "lang": "en", "kind": "multiple_choice", "question": "A nucleus has 11 protons and 11 neutrons. What is its mass number?", "choices": {"A": "21", "B": "23", "C": "24", "D": "22"}, "answer": "Mass number is 22.", "steps": ["A = 11 + 11.", "A = 22.", "Select option D."], "text": "Answer: 22\nSteps:\n1. A = 11 + 11.\n2. A = 22.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0997", "subject": "physics", "topic": "mechanics", "lang": "cs", "kind": "multiple_choice", "question": "Vyber: co je síla krát dráha?", "choices": {"A": "výkon", "B": "práce", "C": "moment", "D": "impuls"}, "answer": "Odpověď je práce.", "steps": ["Jouly sečteny.", "Tedy: práce.", "Vyber možnost B."], "text": "Answer: práce\nSteps:\n1. Jouly sečteny.\n2. Tedy: práce.\n3. Vyber možnost B.\nAnswer: (B)"}
{"id": "phy_0998", "subject": "physics", "topic": "electromagnetism", "lang": "en", "kind": "multiple_choice", "question": "A current of 4 A flows for 55 s. How much charge passes?", "choices": {"A": "200 C", "B": "240 C", "C": "260 C", "D": "220 C"}, "answer": "Charge is 220 C.", "steps": ["Q = 4 A × 55 s.", "Q = 220 C.", "Select option D."], "text": "Answer: 220 C\nSteps:\n1. Q = 4 A × 55 s.\n2. Q = 220 C.\n3. Select option D.\nAnswer: (D)"}
{"id": "phy_0999", "subject": "physics", "topic": "thermodynamics", "lang": "en", "kind": "concept", "question": "Why study thermodynamics?", "choices": null, "answer": "It rules engines, life, and cosmos through energy and entropy laws.", "steps": ["It rules engines, life, and cosmos through energy and entropy laws.", "So the answer stands: It rules engines, life, and cosmos through energy and entropy laws."], "text": "Answer: It rules engines, life, and cosmos through energy and entropy laws.\nSteps:\n1. It rules engines, life, and cosmos through energy and entropy laws.\n2. So the answer stands: It rules engines, life, and cosmos through energy and entropy laws."}
{"id": "phy_1000", "subject": "physics", "topic": "optics", "lang": "en", "kind": "worked_example", "question": "Light travels 55×10⁸ m. Compute the travel time. (c = 3×10⁸ m/s)", "choices": null, "answer": "Time: 18.3 s.", "steps": ["t = d/c.", "t = 55×10⁸ / 3×10⁸ s.", "= 18.3 s."], "text": "Answer: Time: 18.3 s.\nSteps:\n1. t = d/c.\n2. t = 55×10⁸ / 3×10⁸ s.\n3. = 18.3 s."}