تمارين التهدئة وتمارين التمدد مهمة بعد جهاز التجديف.

Yes. This is a normal nominal sentence in Arabic.

The structure is:

• تمارين التهدئة وتمارين التمدد = the subject
• مهمة = the predicate adjective, meaning important
• بعد جهاز التجديف = a prepositional phrase, after the rowing machine / after using the rowing machine

Arabic often omits the present-tense verb to be. So where English says are important, Arabic can simply say مهمة.

This is one of the most important grammar points here.

تمارين is a non-human plural, and in Modern Standard Arabic, non-human plurals often take feminine singular agreement. That is why the predicate is مهمة rather than a plural form.

So even though English says exercises are important, Arabic commonly uses:

• التمارين مهمة = the exercises are important

This is standard Arabic agreement with non-human plurals.

Because of that same agreement rule.

Since تمارين is a non-human plural, Arabic treats it grammatically like a feminine singular for agreement purposes. So the adjective/predicate becomes مهمة rather than مهم.

Compare:

• الطلاب مهمون = the students are important
  
  • human plural -> true plural agreement
• الكتب مهمة = the books are important
  
  • non-human plural -> feminine singular agreement

Because it is the predicate of the sentence, and predicates in Arabic are usually indefinite.

So:

• التمارين مهمة = the exercises are important

not usually:

• التمارين المهمة in this structure

But note that التمارين المهمة is possible in a different structure, where it means the important exercises. That is a noun phrase, not the same kind of sentence.

You can say تمارين التهدئة والتمدد. That would mean cool-down and stretching exercises.

The repeated version:

• تمارين التهدئة وتمارين التمدد

is a bit more explicit and balanced. It clearly presents two separate categories:

• cool-down exercises
• stretching exercises

So the repetition is not required, but it is natural and helps with clarity.

Because this is an iḍāfa construction, often called a genitive construction.

In:

• تمارين التهدئة
• تمارين التمدد
• جهاز التجديف

the first noun usually does not take ال. The definiteness comes from the second noun.

So:

• تمارين التهدئة = literally exercises of the cool-down
• جهاز التجديف = the rowing machine / literally device of rowing

Since التهدئة, التمدد, and التجديف are definite, the whole phrases are definite.

It is another iḍāfa construction:

• جهاز = device / machine
• التجديف = rowing

So جهاز التجديف literally means the machine/device of rowing, which is the normal way to say rowing machine in MSA.

This is very common in Arabic. Instead of making a compound noun the way English does, Arabic often uses this noun + noun structure.

Literally, yes, it is after the rowing machine. But in natural meaning, it usually means:

• after using the rowing machine
• after a rowing-machine workout

Arabic often allows this kind of short, slightly elliptical phrasing, especially in practical or instructional language.

If you wanted to make it more explicit, you could say:

• بعد استخدام جهاز التجديف = after using the rowing machine
• بعد التمرين على جهاز التجديف = after exercising on the rowing machine

They are verbal nouns.

• التهدئة comes from a verb meaning to calm down / make something calmer. In fitness context, it means cool-down.
• التمدد is related to stretching / extending. In fitness context, تمارين التمدد means stretching exercises.

So these are not random vocabulary items; they are standard Arabic ways of expressing workout concepts.

A fully vocalized version would be:

تَمارينُ التَّهْدِئَةِ وَتَمارينُ التَّمَدُّدِ مُهِمَّةٌ بَعْدَ جِهازِ التَّجْديفِ.

A rough transliteration is:

tamārīnu at-tahdiʾati wa-tamārīnu at-tamaddudi muhimmatun baʿda jihāzi at-tajdīfi

A few useful case notes:

• تمارينُ is nominative here because it is the subject
• مهمةٌ is nominative because it is the predicate
• بعدَ is followed by a genitive phrase
• جهازِ التجديفِ is genitive after بعد

Yes. A few natural alternatives are:

• تمارين التهدئة والتمدد مهمة بعد استخدام جهاز التجديف.
• تُعَدُّ تمارين التهدئة والتمدد مهمةً بعد استخدام جهاز التجديف.
• من المهم القيام بتمارين التهدئة والتمدد بعد استخدام جهاز التجديف.

These all mean roughly the same thing, but with slightly different style:

• the first is simple and direct
• the second is a bit more formal
• the third sounds more like advice or instruction

The original sentence is perfectly understandable, but it is a little compact.