Remove the $ Sign before your $note. The dollar Sign is only a convention of the Framework to identify internal Providers,... .
For example try:
var app = angular.module("app", ['ngResource']);
app.factory("note", ['$resource', function($resource){
return $resource("/api/notes/:id", {id:'@id'}, {
query: {method: "GET", isArray: true}});
}
]
);
app.controller("NotesController", function($scope, note){
console.log("I am being constructed");
$scope.notes = note.query();
});