题目

已知五面体ABCDEF中，四边形CDEF为矩形， CD＝2DE＝2AD＝2AB＝4，AC=，． （1）求证：AB平面ADE； （2）求平面EBC与平面BCF所成的锐二面角的余弦值. 答案：（6分） (2) 直线DE,DC,DC两两互相垂直，故以点D为坐标原点，分别以正方向为轴正方向建立空间直角坐标系，则E （0,0,2），A（2,0,0），C（0,4,0），B（2,2,0），F（0,4,2），分别设平面EBC和平面BCF法向量为，，则，取得，同理，  设所求角为，则，即所求锐二面角的余弦值为 （12分）Holidays are really important. Many of us will have childhood memories of summer holidays where we were taken away from home to experience new environments and learn in different ways.But holidays are expensive and, for those on low wages or living on benefits, they are often unobtainable. Even the cheapest holidays require travel and other additional costs that are difficult for many families to meet.For working parents, the long summer break can be a very difficult problem for childcare. When an annual leave allowance amounts to only five weeks, there is a need to spread this across the year. Couples can find themselves taking leave in turn in order to care for children who are on holiday. For some ’ this makes even an affordable family holiday difficult.The schools that I visit in Nottingham are full of experienced staff committed to giving our children a caring and inspiring learning environment. The number of children receiving free school meals is quite large in Nottingham and many schools have breakfast clubs to make sure that children get a healthy start to the day. Most schools undertake programs of group or individual educational support. Schools also have an important role in sofeguaiding children's welfare through the ongoing touch and support with their pupils. During the long summer holidays, much of this is missed.While teachers are holidaying in the UK, many of their pupils spend the whole six weeks on the street where they live. The lack of free school meals for six weeks can result in pressure on a family budget and an inability to afford the inspiring experiences that help children to continue their learning.In setting out its plans for a five-term year, Nottingham City Council (委员会)is seeking to reduce the summer holiday down lo four and a half weeks, with a more balanced five terms of roughly eight weeks, each followed by a two-week break. We believe this will give real “down time" for school staff and pupils alike but will be short enough not to cause a real break in learning.We acknowledge that this change may be difficult for some school staff, particularly whose own children are educated in other authorities. However, this must be weighed against the benefits for city children for whom we all have the greatest duty of care.【小题1】 The passage is probably written by   .A．an experienced teacherB．a working parentC．an inspired studentD．a city council member【小题2】The underlined word "they" in the second paragraph refers to "  ’.A．environmentsB．holidaysC．wagesD．benefits【小题3】It is suggested in the passage that the summer break be reduced to.A．2 weeksB．4.5 weeksC．5 weeksD．6 weeks【小题4】The plans for a shorter summer holiday will help students_____ .A．obtain the cheapest holidays without additional costsB．get a chance to spend six weeks a term with teachers in schoolC．benefit more from the caring and inspiring learning environmentD．have more school days to receive free school meals【小题5】It can be inferred from the passage that   _______.A．working parents can enjoy a five-week break to care for their childrenB．the suggested plans for a five-term school year can hardly be carried outC．the long summer holiday gives teachers and students real "down time"D．some school staff will say “ No" to the plans for a shorter summer holiday