1. Find the center of mass of the masses located as follows: 3 kg at (-2,3), 2 kg at (2,-3), 4 kg at (1,0).

2. Find the center of mass of the region bounded by y = sin x, y =, and between x=0 and x=¹.

3. Find the center of mass of the volume obtained by rotating the region bounded by y = ln x, y = 0, between x = 1 and x = e about the y axis.

4.a) Change the point (-3,-5) to polar form.

b) Change the point (-2,240⁰) to rectangular form.

5.a) Change the equation x² - y² = 2 to polar form.

b)Change the equation r = 3cos u to rectangular form.

6. Sketch the graph of r = 1+ cos 2u:

a) first on r vs q graph

b) then polar graph on xy plane.

7. Find the points of intersection of r₁ = cos u and r₂ = 1 - cos u.

Given A = (3,-2,4) and B = (5,4,-1), find:

8. The vector AB

9. The point P on the line AB such that AP/AB = 3.

Considering the vector A = <1,0,2> and B = <3,-4,2>, find:

10. The unit vector in the direction of A.

11. The projection of A onto B.

12. A=,

B=

13. The angle between A and B.

14. Find a so that U = ai- j and V = 3i + aj are parallel.

10 Points Bonus !!

Change the equation r = sin 2 u to rectangular form.