2D rotations are the most basic form of rotation. 3D rotations cannot be well understood if 2D rotations are not mastered.
A vector is an element that has a magnitude (length) and a direction (the way it is pointing). As shown on Fig. 1 a vector can be represented as an arrow that connects the origin of a system to a certain point that is also part of the system. This means that a vector is part (or is mesured) from a specific system.
(Fig. 1 - 2D vector representantion)
The direction of a vector can be specified in 2 ways
angle,magnitude/components different reference systems (if there is a vector in space, it can be seen differently by different systems depending on how they are located) a vector in 2 different systems rotation matrix for a 2d vector meannings of a 2d rotation matrix (the way said matrix can be seen) inverse of it