Rotation matrix

A rotation matrix is like a magical tool that helps us rotate things in space. Imagine you are holding a piece of paper with a picture on it. Now, if you want to turn the picture around, what would you do? You can rotate that paper and the picture will turn around too! Just like that, the rotation matrix helps us rotate objects in space, but instead of paper, we use numbers.

You might know that there are three axes in space - x, y, and z. Think of them as lines on which we can move things around. When we use a rotation matrix, we are essentially telling the numbers to move around these lines. Each line has a certain angle value associated with it, and if we change these angles, we can change how the object looks in space.

The rotation matrix itself is a 3x3 grid of numbers that represent these angles. The first row tells us how much to rotate the x-axis, the second row tells us how much to rotate the y-axis, and the third row tells us how much to rotate the z-axis.

Now, let's say we have a triangle in space that we want to rotate. We can use the rotation matrix to help us move it around on these axes. We take the triangle's coordinates and multiply them with the rotation matrix. This gives us new coordinates for the triangle, which means it has been rotated in space!

So, to sum it up, the rotation matrix is a tool that helps us rotate objects in space by changing the angles at which they are moving on the x, y, and z axes. It's like moving numbers around on lines to change how the object looks.