问题 解答题

已知动圆经过点A(3,0),且和直线x+3=0相切,

(1)求动圆圆心的轨迹C的方程;

(2)已知曲线C上一点M,且|AM|=5,求M点的坐标.

答案

(1)设动圆圆心C(x,y),

∵动圆经过点A(3,0),且和直线x+3=0相切,

∴动圆圆心到点A(3,0)的距离和到直线x+3=0的距离相等,

∴轨迹为以A为焦点,以x+3=0为准线的抛物线,其方程为y2=12x;

(2)设M(x0,y0),则x0+3=5,∴x0=2.

代入抛物线方程得:y02=24y0=±2

6

∴M(2,±2

6
).

材料题

材料分析题。2008年9月15日,美国第四大投资银行雷曼兄弟宣告破产,标志着美国次贷危机最终演变成全面金融危机。阅读材料,回答问题。

材料一:1932年,美国的国民收入从1929年的874亿美元下降到417亿美元,工业生产1932年比1929年下降46%,财政金融一片混乱,银行存款下降,货币供应量锐减,全国6000家银行倒闭,13万家工商业公司破产。失业工人成几何级数上升,达到1500万,工人工资降低40%。1932年农业收入仅等于1929年的1/2,有宾几百个小农场被迫拍卖,破产的农民大批流入城市。

材料二:(见下图)

材料三:2008年12月6日,美国总统奥巴马在广播讲话中,重申他的最新“经济振兴”计划,透露至少创造250万个就业岗位的5点具体的构想:大规模改造联邦政府办公楼,使这更加节能;大力投资公路和桥梁等基础设施建设;大规模升级学校硬件设施,安装节能系统,创造“21世纪的学校”;在美国各地推广普及网络宽带,让“每个孩子都有机会上网”;改进医院设施,确保这些地方能够运用“前沿科技。”——摘编自“中国新闻网”

材料四:2008年10月24日——25日,第七届亚欧首脑会议在北京举行。亚欧会议45个成员国领导人就应对国际金融危机等重大挑战和深化亚欧合作交换了意见。

2009年4月2日,二十国集团伦敦金融峰会举行,各国领导人求同存异,在对IMF(国际货币基金组织)和世界银行增资、加强金融监督……等一系列问题上达成了一致意见。——摘编自“中国新闻网”

请回答:

(1)据材料一,概括材料二出现的主要背景。据所学知识,指出材料二中“NEW DEAL”的中心措施,并概括“NEW DEAL”实施的重大意义。

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(2)据材料三和所学知识,简要比较奥巴马“经济振兴”计划和材料二中“NEW DEAL”的相似之处。与材料二中“NEW DEAL”相比,该计划有何新特点?

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(3)据材料四,指出国际社会应对金融危机的主要策略。据所学知识,分析采取这种策略的现实原因。

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单项选择题

If those "mad moments"—when you ’can’t remember what your friend has told you or where you left your keys—are becoming more frequent, mental exercises and a healthy brain diet may help.

Just as bodies require more maintenance with the passing years, so do brains, which scientists now know show signs of aging as early as the 20s and 30s. "Brain aging starts at a very young age, younger than any of us had imagined and these processes continue gradually over the years," said Dr. Gary Small, the director of the Center on Aging at the University of California, Los Angeles. "I’m convinced that it is never too early to get started on a mental or brain-fitness program," he added.

In his book, The Memory Bible, the 51-year-old neuroscientist (神经学家) lists what he refers to as the 10 suggestions for keeping the brain young. They include training memory, building skills, reducing stress, mental exercises; brain food and a healthy lifestyle. It’s a game plan for keeping brain cells sparking and neural networks in perfect shape.

"Misplacing your keys a couple of times don’t mean you should start labeling your cabinets. Memory loss is not an inevitable consequence of aging. Our brains can fight back," he said.

Small provides the weapons for a full-scale attack.

Simple memory tests give an indication of what you are up against and tools such as "look" and "connect" are designed to make sure that important things such as names and dates are never forgotten. "So if you wanted to learn names and faces, for example, you meet Mrs. Beatty and you notice a distinguishing facial feature, maybe a high eyebrow," said Small. "You associate the first thing that comes to mind. I think of the actor Warren Beatty so I create a mental picture of Warren Beatty kissing her brow."

Small admits it may sound a bit strange but he says it works. "Mental exercises could be anything from doing crossword puzzles and writing with your left hand if you are right handed or learning a language. It could be anything that is fun that people enjoy doing," he added.

He also recommends physical exercise, a low-fat diet and eating foods rich in fatty acids, such as fish, nuts, and fruits and vegetables high in antioxidants (抗氧化剂) including blueberries and onions in addition to reducing stress.

The "mad moment" in the first paragraph refers to the time when we ().

A. don’t listen to our friends

B. have lost our important things

C. have some mental problems

D. have a bad memory