Habakkuk 1: Can justice come from an unjust nation?

Habakkuk was written before Babylon defeat Judah.
Habakkuk can´t understand how the Lord that is righteous and powerful allow so much injustice:

1-4 The problem as God gave Habakkuk to see it:
God, how long do I have to cry out for help
    before you listen?
How many times do I have to yell, “Help! Murder! Police!”
    before you come to the rescue?
Why do you force me to look at evil,
    stare trouble in the face day after day?
Anarchy and violence break out,
    quarrels and fights all over the place.
Law and order fall to pieces.
    Justice is a joke.
The wicked have the righteous hamstrung
    and stand justice on its head.

The Lord answers that He will deal with the injustice sending Bayblon:

5-11
“Look around at the godless nations.
    Look long and hard. Brace yourself for a shock.
Something’s about to take place
    and you’re going to find it hard to believe.
I’m about to raise up Babylonians to punish you,
    Babylonians, fierce and ferocious—
World-conquering Babylon,
    grabbing up nations right and left,
A dreadful and terrible people,
    making up its own rules as it goes.
Their horses run like the wind,
    attack like bloodthirsty wolves.
A stampede of galloping horses
    thunders out of nowhere.
They descend like vultures
    circling in on carrion.
They’re out to kill. Death is on their minds.
    They collect victims like squirrels gathering nuts.
They mock kings,
    poke fun at generals,
Spit on forts,
    and leave them in the dust.
They’ll all be blown away by the wind.
    Brazen in sin, they call strength their god.”


Habakkuk can´t understand: "how can justice comes from a godless nation?"

12-13
God, you’re from eternity, aren’t you?
    Holy God, we aren’t going to die, are we?
God, you chose Babylonians for your judgment work?
    Rock-Solid God, you gave them the job of discipline?
But you can’t be serious!
    You can’t condone evil!
So why don’t you do something about this?
    Why are you silent now?
This outrage! Evil men swallow up the righteous
    and you stand around and watch!

It is very interesting how Habakkuk argue with the Lord. How can the Holy Lord use a nation such as Babylon. The Lord can't approve evil but now it seems so when He uses Babylon. How can be this happening? In a similar way, there are many questions like that about the world that we live today. How can evil people in places of authority?