5. Iran

1. California voters will decide whether to recall Gov. Gavin Newsom on Tuesday, concluding an idiosyncratic election that has been held in the middle of a pandemic and closely watched as one of the first big indicators of the country’s political direction since President Biden took office. Democrats feel increasingly confident, predicting that Newsom will prevail and avert what would be a disaster for the party in California, the nation's most-populous state. If Newsom is recalled, his likely replacement would be Larry Elder, a conservative talk radio host who has made a career bashing liberal causes. But the fact that the Democratic governor of a state Biden won by nearly 30 percentage points is being forced to fight to hold on to his post has highlighted the vulnerabilities of leaders who seemed well positioned before the coronavirus pandemic. Democrats are trying to energize voters without former President Donald J. Trump on the ballot, and a loss — or even a narrow victory — would raise questions about the political clout of Biden, who campaigned with Newsom on Monday night. The leading Republicans vying to replace Newsom have embraced Trump and his baseless claims of a stolen election, an early signal of the party's unwillingness or inability to distance itself from the former president. (30 pts)

2. Facebook provided a data set to a consortium of social scientists last year that had serious errors, affecting the findings in an unknown number of academic papers, the company acknowledged on Friday. The company used a regular monthly call on Friday with roughly three dozen researchers affiliated with Social Science One, a consortium founded in 2018 that Facebook hails as a model for collaboration with academics, to admit the error and apologize for the impact on their work. The data concerns the effect of social media on elections and democracy and includes what web addresses Facebook users click on, along with other information. The error resulted from Facebook accidentally excluding data from U.S. users who had no detectable political leanings — a group that amounted to roughly half of all of Facebook’s users in the United States. Gary King, a Harvard professor who co-chairs Social Science One, said dozens of papers from researchers affiliated with Social Science One had relied on the data since Facebook shared the flawed set in February 2020. But he said the impact could be determined only after Facebook provided corrected data that could be reanalyzed. (30 pts)

一、圖一中有（1） 、（2） 、（3） 、（4）四個平面結構物，小圓符號代表鉸接或 滾接，否則為剛接。請判定它們為不穩定結構或穩定結構？若為不穩定 結構，請說明不穩定原因；若為穩定結構，請判別其靜不定的次數 R。 （R = 0，即表示為靜定結構。）（20 分）

二、圖二為一水平梁，此梁 AC 段及 BC 段之斷面性質不同，AC 段為 EI、 BC 段則為剛性（EI = ∞），相關尺寸配置如圖二所示。若於梁的 A 端施 加一彎矩 M，試以共軛梁法求解此梁最大的垂直位移及其與 A 點的距 離，另亦求解 A 點之轉角。 （本題以其他方法求解，一律不予計分。） （25 分）  

三、圖三顯示一剛架結構，B 點及 C 點為剛接，剛架尺寸配置及各桿件斷面 之 EI 值如圖所示。若於 CD 桿件中點施加一集中載重 P，忽略各桿件軸 向變形，試用彎矩分配法求解 A 點、B 點、C 點之端彎矩 及及 C 點垂直位移△C，並請繪製此剛架結構受力後之彈性變形圖。（本 題以其他方法求解，一律不予計分。）（30 分）

四、圖四顯示一懸臂梁 AB 與二力桿 BC 於 B 點鉸接處使用一螺旋彈簧連 結，此彈簧勁度為 kS，桿件 AB 之斷面性質為 EI、二力桿件 BC 為 EA。 已知 B 點垂直位移及旋轉之自由度分別為 r1 及 r2，相應之垂直力 R1 為 P、彎矩 R2 為 M。試依據圖中所示之自由度 r1 及 r2，以直接勁度法求此 結構之勁度矩陣；若考慮 M = 0，試求解僅有外力 P 作用下之勁度 矩陣，並請依照  求解 B 點之垂直位移△B。 （本題以其他方法 求解，一律不予計分。） （25 分） （已知：EA/L = EI/L3；kS = 5 EI/L）

(一)試述離心泵的工作原理。 （6 分）

(二)試述往復泵的工作原理。 （6 分）

(三)比較離心泵與往復泵的優缺點。（8 分）

(一)回流比加大對塔頂及塔底產物中酒精濃度的影響。 （5 分）

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