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Wall Warts and What They Do? Answered

We all have wall warts, those (usually) black blocks that plug into AC power mains and output differing voltages and amperages of electricity. I have always thought of them as transformers, changing alternating polarity current into single polarity DC current. Obviously some components in the wall warts do this.

I'd like to know what those components are and how they work. An answer to one of the other questions cautions against connecting wall wart output to a DC circuit without a rectifier. Aren't rectifiers built into wall warts? Isn't changing AC to DC the definition of a rectifier?
And, while on the subject of wall warts, can they be used to power LED strip lights so long as the voltage matches and there is sufficient amperage (current) to supply the LEDs? How does one determine the amperage draw of LED strips? Is it done by the number of LEDs per foot multiplied by the amperage each draws? How does one learn the amperage draw of the various types of LED strips?