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The wife of a senior US military officer shot and killed her 13-year-old son on their way to soccer practice, then returned home and shot her 16-year-old daughter in the head while she studied at her computer, police said.
The woman told detectives she killed the teenagers for being "mouthy".
Julie Powers Schenecker, 50, admitted the killings when officers found her covered in blood at the family home on Friday, a police spokeswoman said.
Ms Schenecker's mother had called police from Texas because she was unable to reach her daughter, whom she said was depressed and had been complaining about her children.
Ms Schenecker's husband, Parker Schenecker, is a US Army intelligence officer stationed at US Central Command headquarters in Tampa, Florida.
Colonel Schenecker was in Qatar at the time, and was told of his children's deaths on Friday, an army spokesman said.
Ms Schenecker left a note detailing plans to kill her disrespectful children and herself.
The note said "they talked back and were mouthy and that she was going to take care of it", a Tampa police spokeswoman said.
"I think we will never understand how or why a mother could take the lives of her children," the spokeswoman said. "That was the only reason she provided to our detectives."
The body of Ms Schenecker's daughter, Calyx Powers Schenecker, was found in an upstairs bedroom. The body of her son, Beau Powers Schenecker, was found in a four-wheel-drive in the garage, police said.
An arrest affidavit said Ms Schenecker shot her son twice in the head "for talking back" while driving him to soccer practice on Thursday night.
She drove home, went inside and shot her daughter in the back of the head while she was doing homework, then shot her in the face, the affidavit said.
Police said investigators believe the children "never saw it coming". Both were killed with a .38-calibre pistol.
Ms Schenecker was arrested on two counts of first-degree murder and remanded in custody.
Her Facebook page says she earned a bachelor's degree in physical education from the University of Northern Iowa.
Sylvia Carroll, who was at high school in Iowa with Ms Schenecker, said she was a popular and athletic girl who starred in basketball in the late 1970s.
They reconnected about a year ago on Facebook. "I'm just in shock," she said. "I can't believe this."
The Schenecker family home is on a cul-de-sac in a gated country club community in north Tampa.