Flipping a vector across the y-axis Say I have a vector A=[2,2] and I want to express it as [-2,2] (pretending I don´t know the coordinates). Notice that this is the same vector flipped over the y axis...How do I do this?
A negative vector simply turns it around...
 A: I'll try to make this clear. There is no number $t$ such that $t(x,y)=(-x,y)$. If you want to use only addition/subtraction/multiplication by scalar your only solution is to take $(x,y)$ and subtract $(2x,0)$ from it.
The good solution is to use the linear map $\alpha : \mathbb{R}^2\rightarrow\mathbb{R}^2:(x,y)\rightarrow(-x,y)$. Associated with this linear map is the matrix I posted in comments :
$$\begin{pmatrix}
  -1 & 0\\
  0 & 1
 \end{pmatrix}$$
I won't explain here why this is the matrix of $\alpha$ but now if you use basic matrix multiplication :
$$\begin{pmatrix}a & b\\ c & d\end{pmatrix} \begin{pmatrix}x\\ y\end{pmatrix}=\begin{pmatrix}ax+by\\ cx+dy\end{pmatrix}$$
You will get :
$$\begin{pmatrix}-1 & 0\\ 0 & 1\end{pmatrix} \begin{pmatrix}2\\ 2\end{pmatrix}=\begin{pmatrix}-2\\ 2\end{pmatrix}$$
Anyway, this is how you do it, I hate giving methods like this without explanation but you should take a linear algebra class or read a book about linear algebra to really understand what's going on here. Keep in mind that this is very basic linear algebra and you will come across this type of thing very quickly in any introductory book/class.
A: Your question mentions "the y-axis", and this implies that you have already chosen a coordinate system that you're going to use to express vectors. So any (simple) answer is going to involve some mention of coordinates, too. There isn't going to be a "coordinate free" answer like there is for reversing (negating) a vector. 
The answer was already given in one of the comments: the "reflection" of the vector $(x,y)$ is the vector $(-x,y)$.
The answer to your hexagon question is $CB=OA$.
