9.4.2. Rotation Matrices

Try these first

1. 1.

   What does a rotation matrix do?

   Hint

   Think about how robots change their orientation.

2. 2.

   Name one property that rotation matrices must have.

   Hint

   What does orthogonal mean in geometry?

3. 3.

   What must be true about the determinant of a rotation matrix?

   • 0
   • 1
   • -1

   Hint

   Recall the importance of preserving object characteristics.

4. 4.

   True or False: Rotation matrices can distort the shape of objects they transform.

   • True
   • False

   Hint

   Think about the properties that define a rotation matrix.

5. 5.

   Consider a 3D object represented by the point (2, 3, 5). If you apply a rotation matrix around the Y-axis by 90 degrees, what will be the new coordinates?

   Hint

   Remember the formula for rotating around the Y-axis!

6. 6.

   You have a rotation matrix R: [[0, -1, 0], [1, 0, 0], [0, 0, 1]]. What rotation does this matrix represent and around which axis?

   Hint

   Think about the signs and the positions of the elements in the matrix.