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

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MATH221 December 2007
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Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.

  •  Q1  •  Q2  •  Q3  •  Q4  •  Q5 (a)  •  Q5 (b)  •  Q6 (a)  •  Q6 (b)  •  Q6 (c)  •  Q7 (a)  •  Q7 (b)  •  Q7 (c)  •  Q8 (a)  •  Q8 (b)  •  Q8 (c)  •  Q8 (d)  •  Q9 (a)  •  Q9 (b)  •  Q9 (c)  •  Q9 (d)  •  QS101 10(a)  •  QS101 10(b)  •  QS102 10(a)  •  QS102 10(b)  •  QS102 10(c)  •  QS103 10(a)  •  QS103 10(b)  •  QS103 10(c)  •  

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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 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!

Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

  • If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
  • If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.

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