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Passage One For more than thirty years after astronauts first set foot on the Moon, scientists have been unable to unravel the mystery of where the Earth’s only satellite came from. But now there is direct evidence that the Moon was born after a giant collision between the young Earth and another planet. Previous studies of rocks from the Earth and the Moon have been unable to distinguish between the two, suggesting that they formed from the same material. But this still left room for a number of theories explaining how—for example, that the Moon and Earth formed from the same material at the same time. It was even suggested that the early Earth spun so fast it formed a bulge that eventually broke off to form the Moon. Franck Poitrasson, and his colleagues at the Swiss Federal Institute of Technology have compared Moon rocks with rocks from Earth and discovered a surprising difference. They analysed the weight of the elements present in the rock using a highly accurate form of mass spectroscopy(光谱研究) that involves vaporising a sample by passing it through an argon (氩) flame. Although they appeared very similar in most respects, the Moon rocks had a higher ratio of iron-57 to iron-54 isotopes(同位素)than the Earth rocks. "The only way we could explain this difference is that the Moon and the Earth were partly vaporised during their formation," says Poitrasson. Only the popular "giant planetary impact" theory could generate the temperatures of more than 1700℃ needed to vaporise iron. In this scenario, a Mars-sized planet known as Theia crashed into Earth 50 million years after the birth of the Solar System. This catastrophic collision would have released 100 million times more energy than the impact believed to have wiped out the dinosaurs—enough to melt and vaporise a large portion of the Earth and completely destroy Theia. The debris from the collision would have been thrown into orbit around the Earth and eventually coalesced to form the Moon. When iron is vaporised, the lighter isotopes burn off first. And since the ejected debris that became the Moon would have been more thoroughly vaporised, it would have lost a greater proportion of its lighter iron isotopes than Earth did. This would explain the different ratios that Poitrasson has found. Previous studies could not distinguish between ______.
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设向量组α1=(a，2，10)T，α2=(-2, 1，5)T，α3=(-1，1，4)T，β=(1，6，c)T．试问：当a，b，c满足什么条件时， (1) β可由α1，α2，α3线性表示，且表示唯一 (2) β不能由α1，α2，α3线性表示 (3) β可由α1，α2，α3线性表示，但表示不唯一并求出一般表达式．
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