1.The owner invested a computer on dec. 1, 2009, worth 75,000. Adjusting entries on Dec. 31, 2009.
=the computer is already used for two years and has a remaining life of 2 years.
2. The furniture is bought dec. 6, 2009. At the end of the month, will there be an adjusting entries?

what will be the adjusting entries.

You will need to compute the depreciation expense for one month.

(Cost of the Asset - Salvage Value of the Asset) / Useful life = Depreciation Expense each year. To compute one month Depreciation you take the Depreciation Expense per year / 12 = 1 month of Depreciation Expense.

The journal entry to record this is:
Debit Depreciation Expense for the amount of 1 month Depreciation
Credit Accumulated Depreciation for the amount