What Is Magnitude and How Is It Calculated?

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Magnitude refers to the size or amount of a quantity, often expressed numerically without regard to direction. For example, if traveling at 5 miles per hour east, the magnitude of velocity is 5 miles per hour. Similarly, a force of 50 pounds has a magnitude of 50 pounds, and an elapsed time of 60 seconds has a magnitude of 60 seconds. Understanding magnitude is essential in various contexts, including physics and everyday measurements. Overall, magnitude quantifies how much of something exists.
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how do you find magnitude

how do you find magnitude?
 
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Magnitude means "How much?". If you are traveling at a velocity of 5 miles per hour east, the magnitude of the velocity is 5 miles per hour. (The direction of the velocity is east). Or if someone pushed you with a force of 50 pounds, the magnitude of the force is 50 pounds. Or if it took you 60 seconds to brush your teeth, the magnitude of the elapsed time is 60 seconds.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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