u******p
发帖数: 13 | 1 请教几题sub math
40 If x,y and z are selected independently and at random from the interval [
0,1], then the probability that x>=yz is
answer: "3/4"
does it use double integral to calculate the volume bounded by the surface
of the unit cubic and x=ys?
51 An automorphism phi of a field F is 1-1 mapping of F onto itself such
that phi(a+b)=phi(a)+phi(b) and phi(ab)=phi(a)phi(b) for all a,b belong to F
. If F is the field of rational numbers, then the number of distinct
automorphisms of F is
(A)0; (b)1; | r****y
发帖数: 1437 | 2
[
I think x
so x
So x>=yz is 1-1/4=3/4?
F
【在 u******p 的大作中提到】
: 请教几题sub math
: 40 If x,y and z are selected independently and at random from the interval [
: 0,1], then the probability that x>=yz is
: answer: "3/4"
: does it use double integral to calculate the volume bounded by the surface
: of the unit cubic and x=ys?
: 51 An automorphism phi of a field F is 1-1 mapping of F onto itself such
: that phi(a+b)=phi(a)+phi(b) and phi(ab)=phi(a)phi(b) for all a,b belong to F
: . If F is the field of rational numbers, then the number of distinct
: automorphisms of F is
| R*********r
发帖数: 1855 | 3 sub题目很少只能硬干的，排除法可以搞定很大一部分，你要把所有选项拿出来。 | R*********r
发帖数: 1855 | 4 1. 1-\int_0^1 \int_{x}^{1}x/ydy dx=3/4
2. phi(a+b)=phi(a)+phi(b)==>对有理数a，phi(a)=ka，phi(ab)=phi(a)phi(b)==>k^2
=k
3. S里面的集合必定是以下四个集合的部分并集：M-A-B，A-B，B-A，A交B，因此最多2
^4=16个 | Q***5
发帖数: 994 | 5 64 Let V be the real vector space of real-valued functions defined on the
real numbers and having derivatives of all orders. If D is the mapping from
V into V that maps every function in V to its derivative, what are all the
eigenvector of D?
answer: All nonzero functions of the form (ke)^(lamda*x), where k and lamda
are real numbers
don't know how to get this?
This seems to simple: you are looking for all functions f\in V, such that D
(f) = \lambda f, where \lambda is some constant. From the d
【在 u******p 的大作中提到】
: 请教几题sub math
: 40 If x,y and z are selected independently and at random from the interval [
: 0,1], then the probability that x>=yz is
: answer: "3/4"
: does it use double integral to calculate the volume bounded by the surface
: of the unit cubic and x=ys?
: 51 An automorphism phi of a field F is 1-1 mapping of F onto itself such
: that phi(a+b)=phi(a)+phi(b) and phi(ab)=phi(a)phi(b) for all a,b belong to F
: . If F is the field of rational numbers, then the number of distinct
: automorphisms of F is
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