All the replies so far made me laugh!
I don't think the OP was cheating in their schoolwork. I took their comment to mean they've kept up with recent trends and know a little about the real internet, and not the TEXTBOOK version. The truth is, web applets and alot of other proprietary software requiring plugin downloads has diminished in favor on the Net. And that's the right way to say it - "diminished in favor" because applets have not technically been deprecated the W3C. With Flash being supported by 97% of the browsers, and 50% of those being the latest version, the dominance of Flash for extended GUI and the rich web experience is not and should not be surpising to anyone.
But in school, applets use Java, a powerful, excellent and common language that is well supported across nearly all major computer and browser platforms. It also demonstrates the basic concepts of coding, compiling and web publishing which is still beneficial to know even if most frameworks and languages are interpreted via CGI, web server modules or "just in time" automated compilation. In some cases it's a matter of outdated textbooks, sure, but also it's a simple case of simplicity in action.
Java is now open source (Sun did this a few years back) and that means schools can save money on licenses since Flash isn't free (ask Adobe), not even to schools with volume discounts.
Flash is also considered proprietary, in that it is it's own patented and self contained framework. It's the antithesis of the open source philosophy as you use a special IDE to create, test, compile and publish. But if you start out with Java, and do it manually (running javac on the server via command line interface, create the HTML yourself, FTP the applet stuff, get the paths right, etc.) then you now have the intellectual skills and "under the hood" knowledge which will only help you with other languages, frameworks and so forth. It helps teach you to be a better developer and to learn the basic pitfalls using a deceptively powerful Java core.
Well, that's the positive spin on it. Sit there and learn, that's my advice, then take a great Flash course and go make the real money. But be sure to add both to your resume' and your brain.
Now if they start to teach you COBOL, or ask you do punch holes in cards, or start adding scotch tape to microfiche --- then your school might be the trouble and not you!
-jim