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6.11. An affine transformation of plane is given by the formulas 
.
Find images of: a) points 
; b) lines 
.
6.12. An affine transformation of plane is given by the formulas 
. Find pre-images of: a) the point 
; b) lines 
.
6.13. Write formulas determining an affine transformation of plane transferring the points 
to 
respectively: 
.
6.14. Find all fixed (immovable) points of the following affine transformation given by formulas:
.
6.15. Write the formulas determining the products 
and 
of the following affine transformations: 
.
6.16. Write the formulas determining the inverse transformation for 
if there is such a transformation.
6.17. Let an affine transformation 
be given. Compose an equation of the image of the following curve: a) 
; b) 
.
6.18. Let an affine transformation 
be given. Compose an equation of the pre-image of the following curve: a) 
; b) 
.
6.19. Write formulas determining an affine transformation transferring the lines 
and 
to the axis of ordinates and the axis of abscissas respectively, and the point 
to the point 
(the point 
does not lie on these lines).
6.20. Find all possible affine transformations of plane transferring the points to respectively: 
, if such transformations exist.
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| Exercises for Seminar 6 | | | Пакетный файл, состоящий из двух команд вызова |