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University of Ottawa Questions & Answers
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- A particle of mass m moves on the x-axis. Suppose the particle moves under the action of a hypothetical force Fx = ax where a > 0 is a constant. At t = 0
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- Consider an isometry f: En En, n 2 given by f(x1,x2,...,xn)=(x1,x2 +1,x3 +2,...,xn +n1). Show that f can not be a reflection.
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- Consider an isometry f:E3 E3 given by f(x,y,z)=(1x,z,y). Find a line L in E3 such that f(L)=L (f maps L to itself). Describe the line L in parametric form.
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- Consider an isometry f:E2 E2 given by f(x,y)=(1+y,1x). Represent f as a composite of reflections and translations only.
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- Find examples of functions f1 : E2 E2 and f2 : E2 E2 such that both f1 and f2 are not isometries but their composite f1 f2 is an isometry (in your examples
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- In each case explain why f : E2 E2 is an isometry. (1) f(x,y)=(1x,2+y) (2) f(x,y)=(y,x+1)
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- In each case explain why f : E2 E2 is not an isometry. (1) f(x,y)=(x2,y2) (2) f(x,y)=(x+y,xy)
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- Consider an isometry f: E^n E^n, n 2 given by f(x_1,x_2,...,x_n) = (x_1,x_2 + 1,x_3 + 2,...,x_n + n1). Show that f can not be a reection Notes: _means
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