Translation:The agencies will be closed tomorrow.
Yes, It is rather inappropriate to have this sentence in this lesson. In German, like in English, you can use participles as adjectives. This type of structure is grammatically referred to as "Zustandspassiv". It is basically used to explain the result of a past action.
Perfekt: Er hat das Fenster geschlossen = He closed the window In future: Er wird das Fenster geschlossen haben = He will have closed the window
Zustandspassiv: Das Fenster ist geschlossen = The window is closed. In future: Das Fenster wird geschlossen sein = The window will be closed.
Zustandspassiv (English: statal passive) is a certain type of passive voice. The statal passive emphasizes the state or result of a passive action rather than the action itself.
In this sentence, if I say that the agencies will be closed in the normal passive ("werden geschlossen werden"), I am referring to the action of them actually closing. If I use the statal passive ("werden geschlossen sein"), I am emphasizing the result--the fact that, at whatever future time, they will be closed.
I think I know why my translation wasn't accepted now.
"Sein" is commonly used for verbs involving a change of state of motion. "Werden" definitely qualifies for that. In fact, what's a better example for that than "will.... be?"
I think that in this case, when a more direct translation such as "will... be" is possible, why not go with it? Probably more encouraged than going back to "haben/have" which is more used for transitive verbs (which makes sense since sein is itself essentially a transitive concept).
I think the way to say "The agencies would have been closed tomorrow" is: "Die Behörden würden/wurden morgen geschlossen haben" but don't quote me on that.
Why in this sentence the auxiliary verb is "sein", but when he asked me to translate "You will be closed tomorrow, won't you?" and I wrote "Morgen wirst du geschlossen sein, oder?" he told me that the correct translation is "Morgen wirst du geschlossen haben, oder?"? What's the difference?
I really do not know why DL turned down your answer but I suspect it was in a lesson where the future and future perfect tenses were being emphasized.(I know - that's not a valid reason!) Anyhow, the translation of DL's reply (with 'haben') means "You will have closed, won't you?"
"Schließen" actually does take "haben" because "schließen" is transitive (http://canoo.net/inflection/schlie%C3%9Fen:V:haben). "Sein" would be used to form the statal passive, which (I think) should be valid in Li-Wei's sentence. I'm not sure why Duo would not accept both "haben" and "sein."
A government agency would mean the entire organization. Government offices could mean the agencies, but also the physical places where the work is done. For instance, when there is a big snowstorm in Washington DC, the government offices sometimes close, but not the agency, which could have offices in other cities.