14.某品牌手機的電池由A,B兩家廠商製造，其中40%是A廠製造、60%是B廠製造。已 知A廠的電池有90%的機率可以正常使用超過一年，而B廠的電池有75%的機率可以 正常使用超過一年。假設某甲有此品牌的手機且電池已經正常使用超過一年，則某甲手 機的電池是A廠製造的機率為_____。（化為最簡分數）

15.已知a>1，且知當0≤x≤2時，的最小值為，則a=_____。（化為最簡分數）

16.在坐標平面上，任給共線三點A,BC,且A,B在C點的同側，若以C為圓心、半徑為r的圓滿足（線段乘積），則稱A,B互為對圓的反演點。設為x2+y2-2x+6y+2=0，則點A(2,-2)對圓的反演點B的坐標為_____。

17.設ABCD,,,為空間中正四面體的四個頂點，另有一點E與點D分別在△ABC所在平面的兩側，且（向量內積）。則cos∠DAE=_____。（化為最簡根式）

19.若T將直線y=x+1上的點都映射到直線y=5x+13上，試求a、b。（非選擇題，6分）

20.（承19題）設P,Q為平面上兩相異點，令P'=T(P)、Q'=T(Q)，試說明為定值， 並求此值。（非選擇題，6分）

1. You are going to enbance a machine, and there are two possible improvements:either make multiply instructions run four times faster than before, or make memory access instructions run two times faster than before. You repeatedly run a program that takes 200 seconds to execute. Of this time, 50% is used for multiplication, 20% for memory access instructions, and 30% for other tasks. Determine the speedup for the corresponding cases. Copy Table I to your answer sheet and fill your answers.Enhancement cases:C1: Improve only multiplicationC2: Improve only memory accessC3: Improve both multiplication and memory accessTable 1.

2. The dynamic power of a processor is related to the capacitive load (C), operation frequency (F) and voltage (V) with this equation Power=CFV2. Suppose we developed a new, simpler processor that has 80% of the capacitive load of the more complex older processor. Further, we can reduce the voltage of the new processor by 20% and let the new processor run at 20% faster frequency. What's the dynamic power of the new processor with respect to the dynamic power of the old processor ?

3. The following C procedure swap is compiled into the corresponding MIPSassembly code. Assume that the parameters v and k, and variable temp are in registers $a0, sal and $to, respectively. Other registers that can be used are St1 and St2. C procedure:Please determine proper values for the operands (OPA, OPB, OPC, OPD). Copy thefollowing table (Table 3) to your answer sheet and fill in the operand values.

4. Figure 4.1 is a basic multiplication hardware and Figure 4.2 is an improvedversion of the basic one.Figure 4.1: Basic multiplication hardwareFigure 4.2: Improved multiplication hardwareThe following statements are possible observations for the improvement:S1: The multiplicand register, ALU, Multiplier register and the Product register are all 32 bits wide；S2: The Product register always shifts right two bits in each iteration；S3: The original Multiplier register disappears and is now placed in the right half of the Product register initially；S4: The left side of the Product register is initially set to zero.S5: The Multiplicand register is initially set to zero.Please copy the following table (Table 4) to your answer sheet and determine if these statements are true or false.

5.The following figure is a simple implementation of a MIPS subset (R-type, 1w, sw, beg). Copy Table 5 to your answer sheet and fill in the corresponding control signal values (0, 1 or X) for instructions 1w (load word) and beg (branch on equal).

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