公職公共管理

.3. (15 points)(a) Construct a field F over Q such l-hal; x7 +2x + 2 has a root, in F. Find the degr

(h) Construct a finite field of 27 eloinctits.

4.(20 poinl.s) Let G =- <a> be a cyclic grovip of order n.【題組】(a)Show f,hat for any d | n, the

【題組】(b)Show filial; if (r, n) = d、tlion ad<ar>

【題組】(c)Show that, tbn subgroup<ar>has order

5.(15 points)(a)Explain why non-trivial group homomorphismexisf

(b)Show (Jiaf; a nori- trivial group bomomorpbismexhibitrig an example.

6 (15 points) Let R be an integral clomam..【題組】(a)Show llmt every prime olcrrient in R is irrexlncib

【題組】(b)Suppose ihnl R is a PID. Show tlmt, every irreducible element in /i! is a prime.

二、（20%，@5分，請算至小數點第二位，四捨五入）Baltics Corpoiation has issued common stock only. The company has been suc

【題組】(B)The inventory turnover

【題組】(C)The average days in inventory.

【題組】(D)Return on common stockholders' equity,

三、（20%，@5 分）Use tlie following information to perform (he calculations btlov (using the indirect met

【題組】(B)Calculate the amount of cash flows from investing activities.

【題組】(D)Calculate the net change in cash.

四、（20%＞@5 分）On January 1，2007，Caldwell Corporation had 75,000 shares of $1 par value common stock is

五、（15%,@5 分)On January I, 2006, Matrix Corporation issued $^00,000, 5%, 5-year bonds dated January 1

二、填充題（計十二格，每格 5 分，共 60 分）：1. 將 1，2，…，100 等 100 個正整數，依右列方式排成一個 10 階方陣［aij］10×10，則【題組】 (1) a77＝ (1) 。

【題組】(2)若 aij＝77，則（i，j）＝ (2) 。

2. 設。若兩個二階方陣 P，Q，使 A＝P＋Q，而 Pt＝P 且 Qt＝－Q，則此二方陣 P，Q的乘積為(3) 。

3. 設 A ＝［aij］n×n是 n 階方陣，且 aij＝i＋j，【題組】(1) 若矩陣 A 所有元素的和為64n2，則 n ＝ (4) 。

【題組】(2) 令n = 10，A2＝［cij］10×10，則 c57＝ (5) 。

4. 設，則A＋A2＋A3＋…＋A2009＝ (6) 。

5. 九章算術(約成於西漢時期)卷八(方程)第一題：「今有上禾三秉，中禾二秉，下禾一秉，實(共)三十九斗；上禾二秉，中禾三秉，下禾一秉，實(共)三十四斗；上禾一秉，中禾二秉，下禾三秉，實(共)二十六斗

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