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Wherever you see her, whether it's kicking a ball on the training field, battering a backhand on the practice court, or grunting her way to a tough win in the high heat on Stadium 3, 19-year-old Victoria Azarenka of Belarus (and now Arizona) always looks hungry. Not in the I-need-to-eat sense, but in the I-need-to-get-better-right-now* sense.

Every morning this week Azarenka has been one of the first players out on the field to work out. She and her trainer, Mark Wellington, begin slowly. Headphones on, she swings her arms forward and backward, then gently tosses and kicks a soccer ball with him. The drills and the ball gradually speed up until both player and trainer are quick-stepping to keep it in front of them. Usually, you'll see players take small breaks during these types of workouts and share a laugh with their trainer. Not Azarenka. When the ball gets past her, she stamps her foot in frustration.

Wellington, an Englishman who is the director of the performance institute at the International Tennis Academy in Delray Beach, Fla., has traveled full-time—42 weeks a year—with Maria Sharapova and Tatiana Golovin in the past. In 2009, he's doing 18 weeks with Azarenka. He says she's closer to Sharapova than Golovin in her intensity. "She's like Maria, she doesn't want to hang out. She wants to play tennis."

While she's already ranked No. 11, Azarenka is still learning. "She loves the fitness work," Wellington says, "but she's just finding out why she's doing it. We have to teach her what the exercises do for her and what she needs to work on. But she's eager to learn. Everything is raw right now." If anything, Wellington says that Azarenka is a more talented natural athlete than Sharapova. She's more comfortable doing different things with the ball than Sharapova was when she was younger. She just needs more of everything: explosiveness, stamina, strength.

Wellington says that Azarenka is in a transition period right now. "She's growing up and she's on the tour full-time, and she wants to control things," he says, "but she still gets frustrated." From Andy Murray to Ana Ivanovic, the issue of career control is a common one on the tours. These are college-age kids coming into their own and figuring out how much distance to put between themselves and their parents or whatever tennis academy or federation was responsible for raising them. Azarenka seems to be in the thick of that process right now.

After her fairly light early-morning workout, she gets down to intense business on the court. While most of her colleagues keep it in cruise control in practice—they've got matches to play later, after all—Azarenka is in full flight, and grunt, the whole time. She leaps into her ground strokes, bangs her racquet on the court when she misses, and doesn't crack a smile. Just when the workout finally seems to be over, she stalks back to the middle of the court for one last session of target practice.

Not surprisingly, one of Wellington's primary jobs is getting Azarenka to manage her intensity efficiently. "At tight spots in a match," he says, "she can expend too much energy."

Azarenka kept her cool on a hot afternoon today, beating Shahar Peer 7-5, 6-4 and keeping up an all-business attitude throughout. She was stern with the ball kids, and with the fans. At 4-4 in the second, something flashed in her eye. Azarenka stopped play and pointed into the stands at the opposite end of the court. One guy thought she was pointing at him, so he took off his hat. Another couple folded up their umbrella. Azarenka only got more frustrated, yelling, "Hello! Hello!" at someone. Finally, a woman took off a shiny plastic badge she was wearing around her neck. It had been a five-minute delay, with a lot of confusion involved, but Azarenka walked back to the baseline and ended the next point with a perfect drop shot. She broke serve and held at love for the match.

As far as her game is concerned, her backhand is her stronger stroke. She hits it well out in front, with a nice forward lean, and full but compact extension. It's Azarenka's forehand that's more problematic. She swoops up on it, at times as if she's throwing a horseshoe, and tends to sail it long; she can also get crossed up with her footwork and end up backing out of the shot. It gets better when she's on defense, when she's reacting and not creating pace. Early on, Peer wrong-footed Azarenka a number of times, and it seemed that she might be able to outfox her less-experienced opponent. But Azarenka proved to be more consistent and willful in pursuit of the advantage in rallies. She's no pusher.

Flaws? While Azarenka may be a better athlete than Sharapova, I don't see the same explosiveness through the court in her shots yet. And even on her excellent forehand, she can get anxious and pull it wide. The serve is serviceable; she has a more fully developed motion than many of the other women. Her best attribute, for the moment, is how deadly serious she is about it all. But this remains a transition, as her trainer says—if she doesn't keep rising in the rankings, will that seriousness turn to self-defeating frustration?

I saw Wellington after the match today, and he wasn't gushing about the win. He said Azarenka had spent too much time behind the baseline, and that the famously slow Indian Wells courts, which he says are playing slower than ever this year, didn’t help her flat strokes. But a learning process is a learning process, and a win is a win. Now Azarenka goes on to face a much stronger opponent, Dinara Safina.

For the moment, though, she just wanted to get something to eat. Wellington counseled her to limit it to a salad, because she had to play doubles soon after. Victoria Azarenka: Still hungry.