A carousel ride rotates in a clockwise direction at a rate of five times per minute. A rectangular gondola has vertices K(1, 1), L(1, 3), M(2, 3), and N(2, 1). What are the coordinates after fifteen seconds? Round to the nearest tenth. Give the coordinates in matrix form.

Question

The answer is:
[ 1 3 3 1]
[-1 -1 -2 -2]

But how did they get the answer? Hope you can figure this out.

Answer 1

12 sec per rotation, so 15 sec means 1 1/4 rotation. So you rotate clockwise 1/4 rotation. 1/4 rotation changes the coordinate one to the clockwise.
1,1 becomes 1,-1
1,3 becomes 3,-1
3,-2 becmes 2,=3
2,1 becmes 1,-2

Do this. Plot the four points on an x,y coordinate graph. Now rotate the coordinate system 90 deg counterclockwise (the same as rotating the points clockwise). Now label the old y axis the new x axis, and the old x axis is now the -y axis, and read the new coordinates and you will get the above.

Answer 2

15 seconds * 5rpm = 5/4 rev

So, after 15 seconds, it has rotated 1 1/4 times.

I am also having trouble getting the given matrix. How does it rotate? What is the axis of rotation?