二、計算題（每題 8 分，共 24 分） 1.設方程式之三根為α 、β 、 γ，試求以 、 、 為三根之三次方程 式。

2.將偶數數列 排列為以下陣列，第i列第 j 行為a ij  ,例如，  a32=  18，試求一般項 αij

3.如圖，有一個底半徑為 5 公分的圓柱體，被一個通過直徑 AB 且與底面夾45° 角的平面所截，試 求所截出的立體體積。

Part 4 Short essay writing 20% Some people argue that studying in a foreign country has many advantages; others think that the disadvantages outweigh the advantages and argue students should stay in their own country to study. Briefly consider both sides of the issue and state which position you support. Give examples to support your arguments.

III: Short essay writing: 1. The following passage is taken from a famous commencement speech. Based on the passage, please discuss: what advice does the speaker try to share with us and what does this passage mean to you? “Climb the mountain not to plant your flag, but to embrace the challenge, enjoy the air and behold the view. Climb it so you can see the world, not so the world can see you. Go to Paris to be in Paris, not to cross it off your list and congratulate yourself for being worldly.”

2. Internationally, people are voicing concern over environmental issues, like air and water pollution, the depletion of natural resources, and the extinction or endangerment of many plant and animal species. Please explain how an individual can alter his or her living habits to protect the environment. Give specific details and examples to support your explanation.

1. What is molar concentration of K+ in a solution that contains 63.3 ppm of K3Fe(CN)6(329.3 g/mol)?(4%)

2. What concentration of sodium chloride in water is needed to produce an aqueous solution isotonic with blood (II=7.70 atm at 25℃)(4%)

3. Calculate the pH of the resulting solution when mixing 75.0 mL of 0.05 M hydrochloric acid with 0.093 g of magnesium hydroxide.( Magnesium:24.3050 g/mol)(4%)

4. At 25℃, calculate the pH of a 0.25 M hydroxylamine hydrochloride solution. The Kb value for hydroxylamine is 9.1 × 10-9. (4%)

5. Calculate the molar concentration of H2SO4 (98.0 g/mol) in a solution that has a specific gravity of 1.84 and is 96.5% H2SO4 (w/w). (4%)

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