Math Help - Factor group of an external direct product

1. Factor group of an external direct product

Find the order of $Z \oplus Z | <(2,2)>$

Now, the elements in $Z \oplus Z$ are (0,0) and (1,1), so the order of it is 2. but I'm confuse about the second one, what is the order of that?

Find the order of $Z \oplus Z | <(2,2)>$
Now, the elements in $Z \oplus Z$ are (0,0) and (1,1), so the order of it is 2. but I'm confuse about the second one, what is the order of that?
Here $\mathbb{Z}\oplus \mathbb{Z} = \{... ,(-2,-2),(-1,-1),(0,0),(1,1),(2,2),...\}$
Write out $\left<(2,2)\right>$ which means $\{...,(-4,-4),(-2,-2),(0,0),(2,2),(4,4),...\}$.
$\left< (2,2) \right> \mbox{ and }(1,1) + \left< (2,2)\right>$.