问题 问答题

求曲面积分I=

dzdx+2dxdy,其中S是球面x2+y2+z2=4外侧在z≥0的部分.

答案

参考答案:记I=[*]dydz+Qdzdx+Rdxdy,则[*]
可考虑用高斯公式计算,但S不是封闭的,所以要添加辅助面.
直接套公式计算也不复杂,将之投影在xOy平面上较方便.
[解法1] 添加辅助面S1=0(x2+y2≤4),法向量朝下,S与S1围成区域Ω,S与S1的法向量指向Ω的外部.在Ω上用高斯公式,得
[*]
用先二后一的求积顺序求三重积分:
[*]
或用球坐标变换来计算:
[*]
[*]
[*]
其中:Dxy:x2+y2≤4.
因此I=4π-(-8π)=12π.
[解法2] S在xy平面上的投影区域是Dxy:x2+y2≤4.因S取上侧,套公式得
[*]
由x2+y2+z2=4,得[*]代入得
[*]
用极坐标变换得
[*]

解析:[考点提示] 曲面积分.

单项选择题

When we think of leadership, we often think of strength and power. But what are these really, and how do they operate

Leadership today is not about forcing others to do things. If this is even possible, it is short term, and tends to backfire. If you order someone to do something against their will, they may do it because they feel they must, but the anger they feel will do more harm in the long term. They will also experience fear.

Fear causes the thinking brain to shut down, making the person unable to function at his or her best. If they associate you with this emotion of fear, they will become less functional around you, and you will have succeeded in not only shooting yourself in the foot, but possibly making a very good employee or partner unable to perform effectively. Fear has no place in leadership.

The way we influence people in a lasting way is by our own character, and our understanding and use of emotion. We can order someone to do something, which may be part of the workday; or we can employ them at the emotional level, so they become fully devoted to the projects and provide some of their own motivation. Today’s workplace is all about relationships as a human being as well as a worker. Everyone produces just a bit more for someone they like. Leaders understand the way things work. They know the paycheck is not the single most motivating factor in the work life of most people.

The true strength of leadership is an inner strength that comes from the confidence of emotional intelligence—knowing your own emotions, and how to handle them, and those of others. Developing your emotional intelligence is the single best thing you can do if you want to develop your relationships with people around you, which is the key to the leadership skills.

An employee may have a feeling of fear in the workplace when ().

A. he is forced to do things

B. be cannot work at his best

C. he feels his brain shut down

D. he thinks his work is too heavy

单项选择题 A1型题