Translation:Do you like soup made with vegetables?
We have two sentence:
Do you like the soup that was made from vegetables?
Read the sentence that is written on the blackboard.
Please, tell me why we use "was" in the first sentence but "is" in the second one, and why it's incorrect if I use "is" in the first sentence and "was" in the second one? Thank you!
I think it is to make the English versions comply with the way that English does aspect. The soup was made in the past, so it's ok to use a past-type construction. However, the sentence is obviously still on the blackboard ("is written"); otherwise, you couldn't ask anyone to read it. The sentence that "was written" on the blackboard would probably mean it had been erased already (unless it had an indication of a specific time it was written in the past, like "yesterday").
You didn't give the whole sentence you used, so I'll add the following: "soup cooked with vegetables" can be ok. Personally, "cooked with" for me would sound better with a couple different types of ingredients listed after it, so I would recommend "made with" in a case like here where there's just one item on the list. "soup cooked of vegetables," however, does not sound natural to me.
Maybe there is a difference between broth made from vegetables versus broth made from meat and vegetables added later?