Question

Translations?

Answer 1

http://en.wikipedia.org/wiki/Affine_transformation

Answer 2

By image matrix they probably just want the transformed vectors as columns of a new matrix.

Answer 3

I suppose the first one is x,y in the columns so if you want to go up 4, you need to add 4 to the y numbers.

You can do similar way for the others, draw pictures to see it easier.

Answer 4

Traingle:
\[\left[\begin{matrix}x_1 & x_2 & x_3 \\ y_1 & y_2 & y_3 \end{matrix}\right] \]

Consider the ordered pairs representing the three points of the triangle. Transform each point and then place the results in a new matrix.