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19. A Carnot engine operates between two heat reservoirs at temperatures of 400 K and 800 K. The maximum efficiency of the engine is (19)

其他申論題

第二大題(SECTION 2):填充題 (Fill-in-the-Blank) 16. A 2 kg block slides down a 30° incline with an acceleration of 2 m/s². The coefficient of kinetic friction between the block and the incline is (16)

17. A particle moves in a potential U(x)=U₀[1-exp(-x²/a²)], where U₀ and a are constants. At x=0, the force acting on the particle is (17)

18. Light in an optical fiber undergoes total internal reflection. If the index of refraction of the fiber is 1.5 and that of the surrounding air is 1.0, the critical angle for the light traveling in the fiber is (18)

20. A circuit consists of a resistor R=10 Ω and an inductor L=1 H in series connected to a direct circuit source of 5 V. The time constant of the circuit is (20)

1. 試求=________。

2. 設函數f(x) =x3+ax2+bx+c，(x ∈ R)，其中 a，b，c 為互不相同的非零整數，且f(a) =a3 ，f(b) = b3，則 a+b +c 為何？

3. 設三次函數，求的值。

4. 在空間中有一四邊形，已知= 2，= 3， = 4， = 5，試求＝？

5. 已知對所有的實數，二次函數 y=bx+c+≥ 0，且 a＜b ，則的最小值為何？

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