Tiling Rectangles with Pentominoes

Some polyominoes can be used to tile rectangles. For example, here is the smallest rectangle that can be tiled by the bent tromino:

1. The L, P and Y pentominoes can each tile a rectangle. What is the smallest possible such rectangle? Show each tiling on grid paper.
2. Tile a 3 by 5 rectangle with:
   1. U and X
   2. V and Z
3. Tile a 4 by 5 rectangle with:
   1. T and Y
   2. U and N
   3. V and F
   4. V and N
4. Tile a 5 by 5 square with:
   1. X and Y
   2. Y and Z
   3. Y and F
   4. L and X
5. Tile a 3 by 10 rectangle with:
   1. U and Y
   2. U and F
6. Find the smallest rectangle that can be tiled with
   1. Y and N.
   2. T and N.
   3. T and W.

This figure shows a rectangle tiled with a single F pentomino, and many P's:

7. What is the smallest rectangle you can tile with a single one of each of the pentominoes, and as many P's as you want?