Can you go to the movies with me tomorrow?
同义句：（Would） you （like to） go to the movies with me?
句意：你是否愿意和我一起明天去看电影?
can you在这里应该是征求对方允许,而不是询问能力.改成用would you like to do来向对方发出邀请.
补充问题：
How about having a rest?同义句：（Why）（not）have a rest?
句意：干嘛不休息一下呢?
改成用why not来提建议.