2.Please determine which the following matrix is a diagonal matrix.
(A)
(B)
(C)
(D)

複選題3.Please select the right following description  (A) = and have the same eigenvalues.(B) If matrix A is diagonalizable, then the column of A are linearly independent.(C) Every orthogonal set of V must be linearly independent.(D) If A is an orthogonal matrix, then A is symmetric

複選題5.There are six vectors shown below. Please determine the right description(A) ,are linear independent(B) , are linear independent(C), are linear independent(D) , are linear independent

6.Your team leader ask you to analyze the result of the particle movement in the frequency domain. You first decide to apply the Fourier Transform to do this job. Please select the right answer after applying the Fourier Transform. (A)π(δ(ω-3))；(B)δ(ω-3)+δ(ω+3)；(C)π(δ(ω-3)+δ(ω+3)；(D)3π(δ(ω-3)+δ(ω+3))

7.While receiving the signal, you adopt a circuit to process this signal. After your analysis, youcan model the circuit by using the following ordinary differential equation (ODE).y(x)+3y(x)+2y(x)= [δ(x-3)+δ(x+3)]Please use the result in the previous problem and the symmetric property to solve the above ODE anddetermine the right y(x).(A) π(δ(ω))；(B)π(δ(ω-3)+δ(ω+3)).；(C)π(δ(ω+3)-δ(ω-3)).；(D)π(δ(ω-3)+δ(ω-3)).

8. Now, you decide to transfer one signal s(x) (i.e., s(x) = )and make the f(x) as the carrie wave. Based on the modulation technique, you can create one new signal r(x) containing the s(x) and f(x). Please describe the formulation of the r(x) in the frequency domain. (A)(B) (C) (D)

9.After your analysis, you find that it is not practical to analyze the phenomenon in thefrequency domain in the continuous time. Afterward, you decide to use Discrete Fourier Transform(DFT) instead. Assume you sample the new created r(x) signal every 2 unit time and collect 4 datafrom time zero (ie., x are 0, 2, 4, and 6 sequentially.) If you know that the DFT can be formulated aswhere the L is the length of the samples and the n indicates the sample number. Please select the rightfollowing result of your analysis in the frequency domain after applying your derived DFT.(A) ；(B) ；(C)；(D)；

10. To facilitate the DFT analysis, you decide to program a DFT code. Besides, you find that you can adopt a matrix to perform this kind of transform. Please determine the proper Fourier matrix below, which can transform a length-4 data sequence from time domain to frequency domain. (A)(B)(C)(D)

1. 依ILO綜合海事勞工公約規定，船上醫藥及醫療設備每隔幾個月須實施定期檢查﹖ (A)十 二 (B)十八 (C)二十四 (D)三十

2. 依據MARPOL 73/78國際公約第二條第(4)項之定義，所謂「船舶」係指哪一項？ (A)在海上環境內航行之任何船隻，包括水翼船、潛水艇以及固定或漂浮的海上平台設 施 (B)在海上環境內航行之任何船隻，但不包括軍事建制之艦艇 (C)在海上環境內航行 之任何船隻，但不包括從事捕魚或養殖作業的非動力船筏 (D)在海上環境內航行之任何 船隻，但不包括固定或漂浮的海上平台設施

3. 下列有關船員之敘述何者正確？ (A)船長為海員 (B)船上實習生具有學生身分，不能視 為船員 (C)船員與海員定義相同 (D)船員包括船長與海員

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