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**1. Homework Statement**

Given a square and the respective distension tensor, ε, find the position on his vortices after the transformation.

ε = 0.1.....0.25

.....0.25.....0.1

**2. Homework Equations**

**3. The Attempt at a Solution**

I got kind of lost in this question. I started thinking that maybe a vortic at the coordinates (a,b) would later be at the position (a',b') given by:

(a',b') = (a,b)ε

This got me some weird results tho, which led me to believe it was wrong.

I later tried to solve it using each component of the tensor alone. I know that the components of the diagonal give me the elongation, therefore I used them to find the positions of the vortices after the elongation. The problem came when I had to deal with the distortion. How can I find the position of the vortices there? I managed to find the position of the vortices that were at either the x axis or y axis, using trigonometry

sin(ε

_{xy})=b'/L , where L is the length of the square after the elongation.

My problem now rests with finding the position of the vortix at (L,L).

Using trigonometry I found that the size of the diagonal,D, after the distortion was:

D = Lcos(π/4-ε

_{xy})

Since the vortix will still have an y coordinate equal to the x coordinate after the distortion I can say that:

2A^2=D^2 , where A will be the position of the vortix after the distortion.

I think my way of solving the problem is correct, however I can't help but think there's a better way... If someone could throw me some light I'd appreciate.