Yes they are
Some are, some aren't. As in any other field, being "good at writing papers" is generally a positive thing and will probably help in your career, but for most engineers it's not a daily part of their work.
Not very, engineers are good at doing things, not explaining things, if they were good at writing papers, they would be managers, but at that time, they would write more and do less in the field. Math is the more important subject at hand, not writing.
No, it's not true, lots of engineers are very good with mathematics, physics and their engineering but they cannot write a good paper for their life.
Yes, most engineers on average have very bad writing skills, however, engineers who can write are worth their weight in gold
Being pretty good at math is almost always a prerequisite skill for becoming an engineer, but it is hardly the only one. Beyond being good at math, engineers have to have strong problem solving skills. Eventually most engineers also find themselves promoted to management positions where people skills, budgeting, and organization become critical. As far as writing skills are concerned - sorry to tell you but good engineers also have to be very good at technical writing. While it may seem like essays and papers are not the same as technical writing, most of the skills of persuasion and analysis that are critical to writing essays and other papers are also necessary elements of technical writing. Most engineers spend a large fraction of their time writing reports - to document their work, to explain it to upper management, convince others of the accuracy of their work, convince others of a course of action based on the work they have done, and to justify expenditures or justify investments in facilities, repairs, new acquisitions, new construction, etc. My experience as an engineer is that I spent about a third of my time doing "engineering" a third of my time writing reports, and a third of my time attending meetings - including presenting the content of my written reports. Bottom line - you need to have BOTH good math AND writing skills to become a good engineer.
Very high, most engineers are not good at writing anyway, they are only good at the math and the numerical and logical processes.
You do not necessarily have to be good at writing to be good at something else. Eventually, however, you will very likely be expected to explain something you've done to someone who doesn't understand the field, and being bad at writing will make such explanations a challenge. The best way to improve your writing skills is to A) take more writing courses than are required for graduation, and B) write as much as possible - essays, papers, articles, etc. Never resign yourself to being a bad writer. If you think or know you are, do what is necessary to remedy the situation.
A fact about engineers might include the fact that most engineers are very good at math problems. Engineers also have a huge variety of fields to work in and are generally paid very well.
Actually engineering is for people that are good at engineering. There are people who are very good at math but would be terrible engineers. There are many kinds of engineers but all engineers have to deal with the real world. Most of them work for companies that expect to make a profit. Most successful engineers find themselves in middle management before long . Many engineers use very little higher math once they go to work. Math for engineers is only a tool for solving problems and it is not the only tool. Most problems are solved by applying what has worked before.
Yes. German engineers have a very good reputation.
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It is important for all engineers to have at least a basic understanding of math. Most very specialized engineers need to have a very good understanding of math in order to do their jobs well and safely.