"Do you wear a hat?"
Translation:너는 모자를 써?
써요 is also polite (just not formally polite), 너 would still not be used to address someone. Only casual (써) and plain forms (쓰니 in this case) can use 너. The Forms of Address section in the tips and notes for the Formal Moods skill (which you can find on the Duolingo mobile/desktop website*, not the app) also talk a bit about this.