教甄家庭教育(家政科)

3.In the circuit of Fig. 3, let R1= R2= 1Ω.C1= 0.2 F, and C2 = 0.1 R (25%)【題組】(a)

【題組】(b)Find the frequency response, (i.e., plot the magnitude and phase of H(jω) versusω，respectivel

4.Find the complete response v0(t) for t＞ 0, in the circuit oiTig. 4 if vs(t) = 10u(i) V and vx(0) =

1,Determine in the circuit of Fig. 1. (25%)

2,The switch in Fig. 2 has been in position a for a long time. At / = 0, it moves to position b. Fin

3.The switch in Fig. 3 has been open for a long time and is closed at t = 0. Find i(t) and v(t) for

4.Given that vs = 10u(t) V in the op amp circuit of Fig. 4 assuming zero initial condition, find vo(

II. Essay Quest ions1.Assign tree sUuciures to the wordsincomprehensible, and disesiabl ishmein and

3.(20%)

2.The following scniences involve transfortnaiion. Indicate ihe rules involved, and give ihe deep st

【題組】(B)Should Harry know whether the bottle might explode?

3.TheEnglish data below provide examples of siress placement on cei.uin verbs.

Show all your work.10 points each.1 • Show that a group G is abelian if and only if x2 = e for any x

2.Prove that Z5is a lie Id.

3.Let G be a group such lhat | G | ＜ 200. Suppose G has subgroups of order 25 and 35, find the order

4.Let G be the set of ail rational numbers except -1. Show that (G,) is a group, where ab = a + b +

5.Let G = ＜a＞ be a cyclic group of order 30，where a is a generator of G. Determine ＜a5＞ and ＜a2＞.

6.Up to isomorphism, Jind all groups of order 4.

7.Show that any group oi'order 35 is eyclic.

8.Find all distinct subgroups of Z l2.

9.Prove that every ideal of the ring of integers is principal.

10.LetG be a group and a and b are h G. Suppose a2 = e and ab4 a = b7. Show that b33 = e, where e is

貳、非選擇題四大題（每大題 10 分）題目一：假設電腦使用 8 位元，2 的補數整數儲存法表現一個整數，請回答下列問題：【題組】（一）10110111 是代表 10 進位多少的整數？【3 分】

【題組】（二）4810轉為 8 位元格式是多少？【3 分】

【題組】（三）這樣的表示法所能表達的整數範圍若以 10 進位表示，其起迄範圍為何？【4 分】以上請列出計算過程。

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