You cannot have more than 1 ng-app directive in the same document. You would need to manually bootstrap the other. Other wise only the first instance of ng-app will be bootstrapped automatically by angular.
Other issue is that there is no provider called $scope2, you need to inject $scope.
Example:-
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>
<div ng-app="app" ng-controller="Ctrl">
  <label>Name:</label>
  <input ng-model="name">
  <label>Age:</label>
  <input ng-model="age">
  <h1>{{ name }}</h1>
  <h1>{{ age * 2 }}</h1>
</div>
<div id="app2" ng-controller="Ctrl2">
  <label>Name:</label>
  <input ng-model="name">
  <label>Age:</label>
  <input ng-model="age">
  <h1>{{ name }}</h1>
  <h1>{{ age }}</h1>
</div>
<script>
  angular.module('app', [])
    .controller('Ctrl', ['$scope',
      function($scope) {
        $scope.name = "Jason";
        $scope.age = "21";
        $scope.$watch('name', function() { // Logs the amount of times name changes
          console.log($scope.name);
        });
      }
    ]);
</script>
<script>
  angular.module('app2', [])
    .controller('Ctrl2', ['$scope',
      function($scope) {
        $scope.name = "John";
        $scope.age = "22";
      }
    ]);
  angular.element(document).ready(function() {
    angular.bootstrap(document.getElementById('app2'), ['app2']);
  });
</script>
Demo
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>
<div ng-app="app" ng-controller="Ctrl">
  <label>Name:</label>
  <input ng-model="name">
  <label>Age:</label>
  <input ng-model="age">
  <h1>{{ name }}</h1>
  <h1>{{ age * 2 }}</h1>
</div>
<div id="app2" ng-controller="Ctrl2">
  <label>Name:</label>
  <input ng-model="name">
  <label>Age:</label>
  <input ng-model="age">
  <h1>{{ name }}</h1>
  <h1>{{ age }}</h1>
</div>
<script>
  angular.module('app', [])
    .controller('Ctrl', ['$scope',
      function($scope) {
        $scope.name = "Jason";
        $scope.age = "21";
        $scope.$watch('name', function() { // Logs the amount of times name changes
          console.log($scope.name);
        });
      }
    ]);
</script>
<script>
  angular.module('app2', [])
    .controller('Ctrl2', ['$scope',
      function($scope) {
        $scope.name = "John";
        $scope.age = "22";
      }
    ]);
  angular.element(document).ready(function() {
    angular.bootstrap(document.getElementById('app2'), ['app2']);
  });
</script>
 
 
If your intention is to use just one module and bind other controllers to it. Then just have one ng-app and register your controller to app1.
Create a module:
 angular.module('app', []);
Register a controller:
 angular.module('app').controller('Ctrl1', ctor);
Demo
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.3.8/angular.min.js"></script>
<div ng-app="app">
  <div ng-controller="Ctrl">
    <label>Name:</label>
    <input ng-model="name">
    <label>Age:</label>
    <input ng-model="age">
    <h1>{{ name }}</h1>
    <h1>{{ age * 2 }}</h1>
  </div>
  <div ng-controller="Ctrl2">
    <label>Name:</label>
    <input ng-model="name">
    <label>Age:</label>
    <input ng-model="age">
    <h1>{{ name }}</h1>
    <h1>{{ age }}</h1>
  </div>
</div>
<script>
  angular.module('app', [])
    .controller('Ctrl', ['$scope',
      function($scope) {
        $scope.name = "Jason";
        $scope.age = "21";
        $scope.$watch('name', function() { // Logs the amount of times name changes
          console.log($scope.name);
        });
      }
    ]).controller('Ctrl2', ['$scope',
      function($scope) {
        $scope.name = "John";
        $scope.age = "22";
      }
    ]);;
</script>