docs(tutorial): update to use `v1.5.x` and best practices

This is a major re-structuring of the tutorial app's codebase, aiming at applying established best
practices (in terms of file naming/layout and code organization) and utilizing several new features
and enhancements (most notably components) introduced in recent versions of Angular (especially
v1.5).

Apart from the overall changes, two new chapters were introduced: one on components and one on code
organization.

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In the process, several other things were (incidentally) taken care of, including:

* Dependencies were upgraded to latest versions.
* Animations were polished.
* Outdated links were updated.
* The app's base URL was changed to `/` (instead of `/app/`).

BTW, this has been tested with the following versions of Node (on Windows 10) and everything worked
fine:

* 0.11.16
* 4.2.6
* 4.4.2
* 5.10.0
* 6.2.0

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This was inspired by (and loosely based on) #13834.
Again, mad props to @teropa for leading the way :)

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**Note:**
The old version of the tutorial, that is compatible with Angular version 1.4 or older, has been
saved on the `pre-v1.5.0-snapshot` branch of
[angular-phonecat](https://github.com/angular/angular-phonecat). The `v1.4.x` version of the
tutorial should be pointed to that branch instead of `master`.

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Related to angular/angular-phonecat#326.
Related to angular/angular-seed#341.

Closes #14416