The first example that came to me was driving.
Suppose you're in a car on a flat, level surface, not moving. Will you remain stationary?
The answer is yes, of course. In order to move the car, you must apply some force (either by manually pushing it, or by making the engine do the hard work for you). This is the basic principle of Newton's 1st.
"An object at rest will remain at rest until another force acts upon it."
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It can help scientists and engineers. The best thing I can come up with for everyday life is that it provides a new way of thinking. It expands your horizons and new information can take your knowledge to the next level.
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how are emeralds use in everyday life
Everyday life is frequently irrational.
Unless your "everyday life" involves work in some area of engineering, you won't use matrices in your everyday life.