15.6

1)IDK

3)
u^2,v -> not one to one, one to one on u>0

13)
3u+4v, u-2v
3   4
1  -2
=-6-4=-10

15)
rsin(t), r-cos(t) -> (1,pi)
sin(t) rcos(t)
1      sin(t)
=sin(t)^2-rcos(t)=sin(pi)^2-1*cos(pi)=0--1=1

17)
rcos(t), rsin(t) -> (4,pi/6)
cos(t)  -rsin(t)
sin(t)   rcos(t)
=rcos(t)^2+rsin(t)^2=4*cos(pi/6)^2+4*sin(pi/6)^2
=4*(sqrt(3)/2)^2+4*(1/2)^2=4*3/4+4*1/4=12/4+4/4=16/4=4

19) IDK
(2,3) (4,1) [0,1]*[0,1]
=4u-2v, u+3v

23) IDK
3u+v, u-2v
a)0,3 0,5  b)2,5 1,7
3  1
1 -2
=-6-1=-7
=105
=126


16.1

1)
goes in direction 1,1 and 1,-1

3)
goes in direction 0,1,0 and 2,0,2

5)
goes in direction to right

7)
-3 to 3 in x
positive x= direction of 3 in x gets longer further from axis
negative x= direction of -3 in x gets longer further from axis

9)
-3 to 3 in y
positive x= direction of 3 to right gets longer further from axis
positive x= direction of -3 to left gets longer further from axis

11)
-1/6 to 1/6 in y and x

17)
C

23)
<xy,yz,y^2-x^3>
div -> y+z+0
i(2y-y)-j(-3x^2-0)+k(0-x)=y,3x^2,-x

25)
<x-2zx^2,z-xy,z^2x^2>
div -> 1-4zx+-x+x^2*2z
i(0-1)-j(z^22x-2x^2)+k(-y-0)=-1,-2xz^2+2x^2,-y

27)
<z-y^2,x+z^3,y+x^2>
div -> 0+0+0
i(1-3z^2)-j(2x-1)+k(1--2y)=1-3z^2,-2x+1,1+2y