This should be a simple question for you guys. I am trying to construct trivial examples of contra-variant and co-variant vectors. Suppose I have a 2D Cartesian system with equal units out the x and y axes, and a vector A with components (2,1). Suppose my prime 2D Cartesian system is parallel, but the units along the x’ axis are twice as long as those in the un-primed (and y’) axes. I think my A’ vector has components (1,1). Is that correct? Is that then a contra-variant vector? What is an example of a co-variant vector? Thanks.