Transitioning from Stage 2 to Stage 3

[LCSphysicist]

Homework Statement

I was studying transformations/rotations in a plane, but i am having trouble to understand the image on the black table. dx' is dx in a rotated frame and R is the rotation matrix

Relevant Equations

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My problem is how to go from the second to the third.

 

[PeroK]

Homework Statement:: I was studying transformations/rotations in a plane, but i am having trouble to understand the image on the black table. dx' is dx in a rotated frame and R is the rotation matrix
Relevant Equations:: \n

View attachment 272773
My problem is how to go from the second to the third.

A rotation matrix is orthogonal.