Science:Math Exam Resources/Courses/MATH221/December 2007/Question 09 (d)

MATH221 December 2007

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Question 09 (d)

On a remote planet, moisture is present in clouds, on the continents, and in the seas. Each year 80% of the cloud moisture falls onto the land and 10% falls into the seas. Each year 15% of the land moisture evaporates directly into the clouds and 65% runs into the seas. Each year 70% of the sea moisture evaporates into the clouds. Assume we know also that the total amount of water or moisture on the planet is 86 trillion litres. A large meteor falls onto the planet, causing all sea water to evaporate into the clouds. (The impact has no other effect on the moisture distribution, but it does cause mass extinction of aquatic species.) Write down the matrix which represents the change in the state vector ${\begin{pmatrix}c\\l\\s\end{pmatrix}}$ caused by the impact.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?

If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint

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Solution
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