109北科大電子_工數 

ㆍ(12%) Find an explicit formula for the sequences defined recursively by

105交大資訊聯招 (6points) Three persons, TC, CC, and YJ, have their own gold. They always divide their own two equal parts and donate to others every day. IC, for example, has 12-kilograms gold today and donate 6 kilograms to Cc and the other 6 kilograms to Y.. If TC has 6 kilograms, CC has 1 kilogram, and YJ has 2 kilograms at first, how many kilograms of gold do CC and YJ have after 365 days?

106交大資訊聯招 (10 points) Political affiliations change from one generation to the next. We consider three parties, labeled D, K, and T. In one generation, membership in D goes 80% to D, 10% to K, and 10% to T； membership in K goes 20% to D, 80% to K, and none to T； and membership in T goes 50% to D, 10% to K, and 40% to T. What is the long-term steady state for the three parties (membership ratios among these three parties)?

(a) (12%) Write down the transition matrix A and calculate its eigenvaluesλ. 

(b) (6%) Assume that the initial market share vector of A, B, and C is，what is the limit as k → ∞? 

說明：請將以下短文中劃底線處之中文句子譯成正確、通順、達意的英文(一)中譯英(8 分)① 近年來，許多發展中國家經歷了社會與經濟的巨大危機。 社會經濟困境改變了能 源方面的投資，並因移動限制嚴重影響產業發展。大多數投資活動因而面臨中斷。 ② 雖然面對政治緊張所帶來的紛亂，有些公司年營收仍創歷史新高。

(二)英譯中(8 分)        Playing sports has a major influence on a person’s health. It brings good qualities to one’s life. ③ Doing exercise properly and correctly and achieving a fitness goal can strengthen sportsmen’s core muscles and boost their athletic performance. However, sporting activities have both good and disruptive effects on one’s health. ④Positive effects from workouts are accomplished primarily through physical activities, but negative impacts of excessive movements include increased injuries and extreme fatigue.

(1) 對圖表的描述與分析：分別描述 iOS 及 Android 系統在此期間市占率的趨勢變化； 並比較兩大系統的市占率差異。

(2) 在購買智慧型手機時，作業系統會是你考量的因素嗎？為什麼？

Please find the eigenvalues and eigenvectors of given

Let and f(s) = s4 - 13s3 + 17s2 - 13s + 87. Please find f(A).

無年度 - 主題課程_向量空間：秩(rank)、零度(nullity)、維度#108952

無年度 - 主題課程_向量空間：基底和維度#108872

無年度 - 主題課程_理工學院機率論：古典機率論#108850

無年度 - 主題課程_向量空間：線性獨立和線性相依#108250

無年度 - 主題課程_理工學院機率論：機率分配（離散型、連續型）#107979

無年度 - 主題課程_向量空間：向量空間和子空間#107951

無年度 - 主題課程_理工學院機率論：多元隨機變數#107950

無年度 - 主題課程_理工學院機率論：單一隨機變數#107935

無年度 - 主題課程_行列式和線性方程式：線性方程式#107934

無年度 - 主題課程_線性映射：基底變換和座標變換#107933