How to access DOM of active tab w/ chrome extension

Question

So far I'm able to retrieve the url of the active page, but how can I get the DOM of the page to use jquery selectors on it?

      chrome.tabs.query({
          active: true,
          lastFocusedWindow: true
      }, function(tabs) {
          var tab = tabs[0];
          console.log(tab.url);
      });