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A two-dimensional vector's initial point is \((3,-2)\) and the vector has a magnitude of \(12.\) This vector forms a \(45^{\circ}\) angle with the \(+x\) direction. What is the terminal point of the vector?

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An object on a tabletop moves in a straight line, in a direction that forms a \(60^{\circ}\) angle with a ruler. The position of the object read from the ruler was \(10\text{ cm}\) when it started moving. The object then stops when its position read from the ruler is \(32\text{ cm}.\) What is the displacement of the object?

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