Mayer’s visitor was Meredith Perry, a 22-year-old University of Pennsylvania grad who had cold-emailed Mayer with an investment opportunity: Perry had discovered a way to wirelessly charge cell phones and other electronic devices by transmitting ultrasound from a plug-in device. “It will be the WiFi of energy,” Perry wrote to Mayer about her product, uBeam.

“I was shocked that she responded,” says Perry, who does not have an engineering background (she studied paleobiology and astrobiology at Penn). She had researched her idea via Google and Wikipedia, so it was quite a thrill to pitch to Google’s famed product exec at the company’s Silicon Valley headquarters.

And within 15 minutes of the two women meeting, Mayer committed to invest in her startup.

“It was probably twelve minutes,” Mayer told me earlier this month over breakfast in Palo Alto. (Our breakfast happened to be the day before the Yahoo board offered Mayer the CEO job—and no, I had no clue about her impending career change or her pregnancy).

“It was the shortest meeting I ever had with anyone,” recalls Perry about her June 29 visit with Mayer, amidst all her requisite networking since coming up with her idea for uBeam in October 2010. “I went in with my iPad and I showed her some images that explain how the uBeam product might be used.”

Perry’s take on Mayer: “She is an extremely efficient person who is able to size up not only opportunities but concepts and problems very quickly.”

That management style will be an asset at Yahoo, where Mayer, who is known for decisiveness, must figure out a.) What is Yahoo? and b.) 1,000 other things.

Meanwhile, angel investing is emerging as one of Mayer’s spare-time passions. She has put her money (she won’t say how much) into a dozen or so startups, including One Kings Lane, Minted, Square, Uber, and now uBeam.

The secret to getting Mayer to buy into your business? “It’s about the idea,” she said at our breakfast. “The idea has to address a real user problem and be able to be easily explained.” She added: “You want someone capable and competent technically. But I also pay a lot of attention to the vibe I get from the founder.”

As for Perry, she has proven herself determined and resourceful. She came up with a big idea that addresses a real need, built a prototype with off-the-shelf parts and cheap engineering help, and raised $750,000 from an impressive lineup of seed investors. Besides Mayer, uBeam’s investors include Andreessen Horowitz, Founders Fund, and Tony Hsieh, the CEO of Zappos (AMZN).

Now comes lots of work and many skeptics to overcome before Perry delivers her “game-changing technology,” as she calls uBeam, to customers–potentially airports, retailers like Starbucks (SBUX) and Barnes & Noble (BKS), and consumers who long to cut their cords, so to speak, and charge their gadgets remotely. To see Perry talking about uBeam, watch her Tedx Talk below.