22. Three sinusoidal waves of the same frequency travel along a string in positive direction of an x axis. Their amplitudes are y₁ ,y₁/ 2and y₁/3 , and their phase constants are 0, π/2, and π, respectively. What is the phase constant of resultant wave?
(A) 30°
(B) 37°
(C) 45°
(D) 53°
(E) 60°

18. The potential energy function of a particle moving in one dimension is U=kx2e−x2/a2where  a = 7.50nm . At what value of x is a point of stable equilibrium located? (A) 6.81 nm (B) 7.50 nm (C) 7.80 nm (D) 11.03 nm (E) 12.62 nm

19. A proton with speed  v = 3.00×105m/s orbits just outside a charged sphere. The radius of the orbit is 1.0 cm. What is the charge on the sphere? (The mass of a proton is 1.67×10−27kg.) (A)1.04×10−9C  (B)3.47×10−8C (C)6.23×10−8C (D)6.50×10−8C (E)8.28×10−7C

20. A 1.0µF capacitor with an initial stored energy of 0.50 J is discharged through a 1.0 MΩ resistor. What is the current through the resistor when the discharge starts? (A)1.0×10−3A  (B)2.0×10−3A  (C)1.0×10−2A  (D)2.0×10−2A  (E)5.0×10−2A 

21. A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half-submerged in a liquid of density 800kg/m3 . What is the density of the material of which the sphere is made? (A)1.1×103kg/m3  (B)1.3×103kg/m3(C)1.8×103kg/m3 (D)2.4×103kg/m3 (E)4.8×103kg/m3

23. A girl is sitting near the open window of a train that is moving at a velocity 10.00m/s to the east. The girl’s uncle stands near the tracks and watches the train move away. The locomotive whistle emits sound at the frequency of 500.0 Hz. The air is still. What frequency does the uncle hear? (The speed of sound is 343m/s.) (A) 471.7 Hz (B) 485.8 Hz (C) 500.0 Hz (D) 515.0 Hz (E) 530.0 Hz

24. Two point charges q1=2.1×10-8C and q2 = −4q1 are fixed in two places 50 cm apart. The point charge  q1 is at the right side of  q2 . Find the point at which the electric field is zero, along the straight line passing through the two charges. The point is . (A) 50 cm to the right of  q1  (B) 50 cm to the left of  q2  (C) 100 cm to the right of  q1  (D) 100 cm to the left of q2  (E) The middle point between  q1 and  q2

25. A 5.0 g marble is fired vertically upward from a spring gun. The spring must be compressed 8.0 cm if the marble is to just reach a target 20 m above the marble’s position on the compressed spring. What is the spring constant of the spring? (A) 1.6 N/cm (B) 1.8 N/cm (C) 2.5 N/cm (D) 3.1 N/cm (E) 6.2 N/cm

1. 數列 共有十項，且其和為240，則 之值為(A)30(B)120 (C) 130 (D) 185 (E) 218

 2. 令 ，試問下列哪一個選項是對的？ (A)a=-1   (B)(C) (D)(E)

      3. 已知f(x)，g(x) 是兩個實係數多項式，且知f(x) 除以g(x) 的餘式為x4-1 。試問下列哪一個選項不可能是 f(x)與g(x) 的公因式？ (A)5 (B)x-1 (C)x2-1 (D)x3-1 (E)x4-1