Rotation Math

In English, Rotation means to turn around an object around a center. When an object rotates around a centric Point then it is called as rotation. When any object rotates in three dimensional space about an imaginary line we call it as rotation. Just like this, we can give many definitions for a rotation. If we want to see the real world example of a rotation then we can take an example of earth. Earth revolves around the sun, this is also rotation. Moon revolves around the earth, it is also called rotation. Now the meaning of rotation is clear to you.
 
Now talk about the rotation in Math. In mathematics, when a rigid object revolves around the fixed point then it is called as rotation. It is just opposite of translation. We know that in translation the coordinates of an object changes and it moves from its origin to the destination location. When an object moves it could be either rotation or translation. When the object drags from one Position to another then it is translation and when is rotates around a fix point then it is rotation.
There are various application of rotation in math. Rotations math is also a type of transformation math. If coordinates are given then we can find the rotation from transformation.
Some instructions:
1: Point  the coordinates on plane on x and y axis.
2: If we want to rotate the object 90 degree then just swap the x and y axis. And we will get new coordinates.
3: If we want to rotate 180 degree then there will be no swapping between x and y axis.
We have to change the positive axis into negative and  negative to positive.
4: If we move the object 360 degree then we will be at the initial coordinates, there will be no change in any coordinate.