Translation:This is a cheese knife; this is a fish knife.
Well, according to "The Phonetics of Russian" (Jones Ward, 2011), it depends on the context. If the я is followed by a palatalised (soft) consonant, it's probably going to be expressed as [jæ]. And in very rapid speech, the vowel could sound even higher (close to [jε]).
Native speakers (of Russian) would be the last people to realise this – that's only natural! But just compare the /a/ sound in сядь (sit!) to the one in сад (garden).
In this example, there is actually a slight difference in vowel quality, (probably due to the anticipation of the devoicing of the s in сыра, to be really pedantic). But I imagine Guido's question was more general, and the answer is yes, it does vary a little with the context.
I put "this is cheese knife; this is a knife for the fish" and the correct solutions were: "This is the knife for cheese; it's a knife for the fish." and " This is a cheese knife; this is a fish knife." Shouldn't mine also be accepted since it's basically a mix of the two?
Technically both are wrong. Well, yours is changing это's part of speech in the translation, DuoLingo's is just weird because you typically wouldn't use "the" if describing something's general function.
"This knife" would be этот нож, but here it just says "это нож", meaning "it is" or "this is" a knife.