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In your example '由' means 'by'. To give you more examples, 发动机是由蒸汽驱动的。 The engine is driven by steam. 这首歌是由歌手自己创作的。 The song is written by the singer himself. 小区里的足球场是由大家共同维护的。 The soccer field in the neighborhood is maintained by the community.
了 and 到/著(着) (zháo) serve different functions in sentences. 了 used after verbs implies a sense of "stopped, finished,completed, or done" on the action. 到 and 著(着) used after verbs indicate the result of the action. 找(不/得)着, 找(不/得)到 够(不/得)着, 够(不/得)到 吃(不/得)着, 吃(不/得)到 I can't really tell the difference between 到 and 著(着), but it seems to me ...
Since your difficulty relates more to the differences between 着(zháo) and 到(dào), I will just concentrate on these two in cases where they are used as a complement after a verb to indicate that a goal has been attained or that there is a result. Although both 着 and 到 are used for similar purposes, there are differences, and often, one is preferred over the ...
In your example 「运输问题由他们解决」 is similar to 「运输的问题是他们的责任」. They just state the fact. But 「让他们解决运输的问题」 is more like a suggestion or an order. As @NS.X says, in this situation 「由」 means "by". But these two statements 「运输问题由他们解决」 and 「运输问题*是*由他们解决*的*」 have differences in the tense. 「运输问题由他们解决」 means "the transportation is to be done by them", while 「运输问题是由他们解决的」 ...
I'm not sure if translation questions should be on-topic or not, but I think a literal "Rocket minesweeper" or "missile minsweeper" would be appropriate. Military vehicles don't usually have elegant names. I found one example of the term "rocket minesweeper" specifically referring to a Chinese military vehicle.
After searching on google I found "Minesweeping Rocket System" to be a somewhat official translation to "火箭扫雷车".
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