Rotations
We want to study how to write a rotation as a 2 x 2 matrix.
We will treat is as a "black box" with inputs and outputs below.
You can adjust the angle of the rotation. Once chosen, you can vary the input and see how the output changes.
Set the angle of rotation to 30 degrees. Test how the "black box" changes the input vector . Move the input to be the vector . Write the output vector below. Enter as two numbers vertically: Example 0.345 0.222
Set the angle of rotation to 30 degrees. Test how the "black box" changes the input vector . Move the input to be the vector . Write the output vector below. Enter as two numbers vertically: Example 0.455 0.622
Now put the two answers from above together. What will be the transformation which rotates by 30 degrees? Write as a 2 x 2 matrix: Example: 0.345 0.455 0.222 0.622