Yes, quite a lot.
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For Physics and Engineering yes, but not so much for Chemistry.
Domains and ranges are commonly used in fields such as mathematics, computer science, economics, physics, and engineering. In mathematics, domains and ranges help define the inputs and outputs of functions, which are essential for solving equations and analyzing data. In computer science, domains and ranges are used in programming to determine the scope and limits of variables and functions. In economics, domains and ranges help model relationships between variables in economic systems. In physics and engineering, domains and ranges are crucial for understanding the behavior of physical systems and designing solutions based on specific input-output relationships.
Because they are based more on theory than numbers and facts
Lots and lots and lots. Just off the top of my head, anything that uses quantum physics is based off of Hilbert space theory and operator analysis, which are both (older) fields of math.
No, mathematics and writing skills are completely separate skill sets, most people are either good at one or the other, few are good at both. It's a good idea to work on your writing skills but in most math based jobs like accounting and engineering, you don't need writing skills as much as your mathematical skills.