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• 5. Consider the multiplicative group ().【題組】(a) What is the order of the group? Why?
• 15. 設平面向量和互相垂直，且。若的長度為 6，則的長度為______。（化成最簡根式）
• (b) Buler's Theorem. For each n Ezt,n ＞ 1, and each a EZ, prove that if gcd(a,n) = 1,then (a中(n
• 【題組】5.2 Find matrix P that makes matrix A diagonal.
• 【題組】(b) Find the inverse of 25.
• 6. Let (ZxZ,⊕) be the group with (a, b)⊕(c, d) = (atc+2, 6+d-2) for any (a, b), (c, d) ∈ ZxZ wherea+
• 【題組】(b) What is the identity of the group?
• 【題組】(c) What is the inverse of (a, b)?
• 【題組】(d) [8%] Let (G, +) be an additive group and let h: ZxZ → G be a group homomorphism whereh(3, 2)
• 1. 動員準備機制則可區分為「物資動員」及「軍事動員」兩個子系統。(A)O(B)X
• 【題組】5.3 Are the both dragonized as well? If yes, please prove your reason.
• (12) (10pt) Calculate the matrix function, where the matrix M is defined as
• 3. The matrix is 【題組】3.1 Find the characteristic polynomial.
• 6. Let matrix . Please decompose the A by using SVD decomposition.
• 7. (Algorithm points) In each of the following, . Solve for  relative to the given set ,and determin
• 9.After your analysis, you find that it is not practical to analyze the phenomenon in thefrequency d
• 51. 進入公共場所時，應實施消防安全診斷，以確保安全，不合格的場所就應該拒絕前往。(A)O(B)X
• 【題組】3.2 Find the eigenvalues,
• 【題組】3.3 And Find the associated eigenvectors.
• 4. Using Laplace transform and showing the details of your work, solve the initial value problem.y1&
• 1. 目前　(A)韓國　(B)美國　(C)菲律賓　(D)中國大陸　與日本均涉入我國釣魚臺列嶼爭議。
• 5.Find the general solution of the following differential equation. y"+4y'+4y=sin2x
• 2 梯間垂直放樣作業方法，下列何者不包括在內？(A) 水準儀照準。(B) 垂球垂準。(C) 雷射垂準器。(D) 經緯儀照準。
• 3 有關線路工程，下列敘述何者不恰當？(A) 線路工程是指長寬比很大的工程。(B) 包括公路、鐵路、運河、水明渠、輸電線路、各種用途的管道工程等。(C) 主要有勘測設計階段的測量與施工放樣的測量。(D
• 4 重型施工架與輕型工作架，係依據施工架下列使用分類？(A) 使用目的。(B) 使用型式。(C) 所用材料。(D) 使用運輸。