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Unformatted text preview: The University of Sydney Math3061 Geometry and Topology Web page: www.maths.usyd.edu.au/u/UG/SM/MATH3061/ 2009 Tutorial 1 1. (Revision) ( i ) Given that A = (1 , 1), B = (2 , 3) and C = (4 , 5), find AB , BC and CA . Check your answers by calculating the sum of these three vectors. ( ii ) Find an equation for the line through the point (1 , 1) in the direction given by the vector bracketleftbigg 2 3 bracketrightbigg . 2. Determine (in each case) if the given formula defines as a transformation of the plane, and if it does, find a formula for the inverse transformation - 1 . ( i ) ( x,y ) = ( y,x + 2), ( ii ) ( x,y ) = (ln x,y ), ( iii ) ( x,y ) = ( x 2 y, y ), ( iv ) ( x,y ) = ( x,y + x 2 ). 3. Determine which of the transformations in the previous question are isometries. 4. Given that the transformations and are defined by the formulas ( x,y ) = ( x + y,y ) , ( x,y ) = ( x 2 y, y ) , find formulas for and...
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